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# Line 1 | Line 1
1 < \documentclass[journal = jpccck, manuscript = article]{achemso}
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75 < \usepackage{natbib}
76 < \usepackage{setspace}
8 < \usepackage{xkeyval}
9 < %%%%%%%%%%%%%%%%%%%%%%%
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75 > \documentclass[10pt]{article}
76 > % amsmath package, useful for mathematical formulas
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78 + % amssymb package, useful for mathematical symbols
79   \usepackage{amssymb}
80 < \usepackage{times}
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114 > \usepackage[labelfont=bf,labelsep=period,justification=raggedright]{caption}
115   \usepackage[version=3]{mhchem} % this is a great package for formatting chemical reactions
116   \usepackage{url}
117 + \usepackage{graphicx}
118  
119 < \title{Interfacial Thermal Conductance of Alkanethiolate-Protected Gold
120 <  Nanospheres}
119 > % Use the PLoS provided BiBTeX style
120 > \bibliographystyle{plos2009}
121  
122 < \author{Kelsey M. Stocker}
123 < \author{J. Daniel Gezelter}
124 < \email{gezelter@nd.edu}
125 < \affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\
30 < Department of Chemistry and Biochemistry\\
31 < University of Notre Dame\\
32 < Notre Dame, Indiana 46556}
122 > % Remove brackets from numbering in List of References
123 > \makeatletter
124 > \renewcommand{\@biblabel}[1]{\quad#1.}
125 > \makeatother
126  
127  
128 < \keywords{Nanoparticles, interfaces, thermal conductance}
128 > % Leave date blank
129 > \date{}
130  
131 < \begin{document}
131 > \pagestyle{myheadings}
132  
133 < \begin{tocentry}
40 < \center\includegraphics[width=3.9cm]{figures/TOC}
41 < \end{tocentry}
133 > %% Include all macros below. Please limit the use of macros.
134  
135 < \newcolumntype{A}{p{1.5in}}
44 < \newcolumntype{B}{p{0.75in}}
135 > %% END MACROS SECTION
136  
137  
138 < \begin{abstract}
138 > \begin{document}
139 >
140 >
141 > % Title must be 150 characters or less
142 > \begin{flushleft}
143 > {\Large
144 > \textbf{Interfacial Thermal Conductance of Thiolate-Protected
145 >  Gold Nanospheres}
146 > }
147 > % Insert Author names, affiliations and corresponding author email.
148 > \\
149 > Kelsey M. Stocker,
150 > Suzanne Kucera,
151 > J. Daniel Gezelter$^{\ast}$
152 > \\
153 > 251 Nieuwland Science Hall, Department of Chemistry and Biochemistry
154 > University of Notre Dame, Notre Dame, Indiana 46556, USA
155 > \\
156 > $\ast$ E-mail: gezelter@nd.edu
157 > \end{flushleft}
158 >
159 > % Please keep the abstract between 250 and 300 words
160 > \section*{Abstract}
161    Molecular dynamics simulations of alkanethiolate-protected and
162    solvated gold nanoparticles were carried out in the presence of a
163    non-equilibrium heat flux between the solvent and the core of the
# Line 64 | Line 177 | Notre Dame, Indiana 46556}
177    the surface of the particle into the bulk. This mode of heat
178    transfer is reduced by slow solvent escape rates, and this effect was
179    observed to lower the interfacial conductance for the longer-chain ligands.
67 – \end{abstract}
180  
181 < \newpage
181 > % Please keep the Author Summary between 150 and 200 words
182 > % Use first person. PLOS ONE authors please skip this step.
183 > % Author Summary not valid for PLOS ONE submissions.  
184 > %\section*{Author Summary}
185  
186 + %\documentclass[journal = jpccck, manuscript = article]{achemso}
187 + %\setkeys{acs}{usetitle = true}
188 +
189 + % \usepackage{caption}
190 + % \usepackage{geometry}
191 + % \usepackage{natbib}
192 + % \usepackage{setspace}
193 + % \usepackage{xkeyval}
194 + % %%%%%%%%%%%%%%%%%%%%%%%
195 + % \usepackage{amsmath}
196 + % \usepackage{amssymb}
197 + % \usepackage{times}
198 + % \usepackage{mathptm}
199 + % \usepackage{caption}
200 + % \usepackage{tabularx}
201 + % \usepackage{longtable}
202 + % \usepackage{graphicx}
203 + % \usepackage{achemso}
204 + % \usepackage{wrapfig}
205 + %
206 +
207 + % \title{Interfacial Thermal Conductance of Alkanethiolate-Protected Gold
208 + %   Nanospheres}
209 +
210 + % \author{Kelsey M. Stocker}
211 + % \author{Suzanne Kucera}
212 + % \author{J. Daniel Gezelter}
213 + % \email{gezelter@nd.edu}
214 + % \affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\
215 + % Department of Chemistry and Biochemistry\\
216 + % University of Notre Dame\\
217 + % Notre Dame, Indiana 46556}
218 +
219 +
220 + % \keywords{Nanoparticles, interfaces, thermal conductance}
221 +
222 + % \begin{document}
223 +
224 + % \begin{tocentry}
225 + % \center\includegraphics[width=3.9cm]{figures/TOC}
226 + % \end{tocentry}
227 +
228 + % \newcolumntype{A}{p{1.5in}}
229 + % \newcolumntype{B}{p{0.75in}}
230 +
231 +
232 + % \begin{abstract}
233 + %   Molecular dynamics simulations of alkanethiolate-protected and
234 + %   solvated gold nanoparticles were carried out in the presence of a
235 + %   non-equilibrium heat flux between the solvent and the core of the
236 + %   particle.  The interfacial thermal conductance ($G$) was computed for
237 + %   these interfaces, and the behavior of the thermal conductance was
238 + %   studied as a function of particle size and ligand chain length. In
239 + %   all cases, thermal conductance of the ligand-protected particles was
240 + %   higher than the bare metal--solvent interface.  A number of
241 + %   mechanisms for the enhanced conductance were investigated, including
242 + %   thiolate-driven corrugation of the metal surface, solvent mobility
243 + %   and ordering at the interface, and ligand ordering relative to the
244 + %   particle surface.  The shortest and least flexible ligand, butanethiolate,
245 + %   exhibited the highest interfacial thermal conductance and was the
246 + %   least likely to trap solvent molecules within the ligand layer.  At
247 + %   the 50\% coverage levels studied, heat transfer into the solvent
248 + %   relies primarily on convective motion of the solvent molecules from
249 + %   the surface of the particle into the bulk. This mode of heat
250 + %   transfer is reduced by slow solvent escape rates, and this effect was
251 + %   observed to lower the interfacial conductance for the longer-chain ligands.
252 + % \end{abstract}
253 +
254 + % \newpage
255 +
256   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
257   %               INTRODUCTION
258   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
259 < \section{Introduction}
259 > \section*{Introduction}
260  
261   Heat transport across various nanostructured interfaces has been
262   the subject of intense experimental
# Line 150 | Line 335 | solvent interface.
335   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
336   %               STRUCTURE OF SELF-ASSEMBLED MONOLAYERS ON NANOPARTICLES
337   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
338 < \subsection{Structures of Self-Assembled Monolayers on Nanoparticles}
338 > \subsection*{Structures of Self-Assembled Monolayers on Nanoparticles}
339  
340   Though the ligand packing on planar surfaces has been characterized for many
341   different ligands and surface facets, it is not obvious \emph{a
# Line 190 | Line 375 | section.
375   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
376   %               NON-PERIODIC VSS-RNEMD METHODOLOGY
377   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
378 < \subsection{Creating a thermal flux between particles and solvent}
378 > \subsection*{Creating a thermal flux between particles and solvent}
379  
380   The non-periodic variant of VSS-RNEMD\cite{Stocker:2014qq} applies a
381   series of velocity scaling and shearing moves at regular intervals to
# Line 235 | Line 420 | the primary quantity of interest.
420   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
421   %               INTERFACIAL THERMAL CONDUCTANCE
422   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
423 < \subsection{Interfacial Thermal Conductance}
423 > \subsection*{Interfacial Thermal Conductance}
424  
425   As described in earlier work,\cite{Stocker:2014qq} the thermal
426   conductance of each spherical shell may be defined as the inverse
# Line 260 | Line 445 | interfacial thermal conductance of the ligand layer.
445   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
446   %               FORCE FIELDS
447   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
448 < \subsection{Force Fields}
448 > \subsection*{Force Fields}
449  
450   Throughout this work, gold -- gold interactions are described by the
451   quantum Sutton-Chen (QSC) model.\cite{PhysRevB.59.3527} Previous work\cite{kuang:AuThl} has demonstrated that the electronic contributions to heat conduction (which are missing from the QSC model) across heterogeneous metal / non-metal interfaces are negligible compared to phonon excitation, which is captured by the classical model. The hexane
# Line 284 | Line 469 | surface.\cite{hautman:4994}
469   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
470   %               SIMULATION PROTOCOL
471   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
472 < \subsection{Simulation Protocol}
472 > \subsection*{Simulation Protocol}
473  
474   Gold nanospheres with radii ranging from 10 - 25 \AA\ were created
475   from a bulk fcc lattice and were thermally equilibrated prior to the
# Line 304 | Line 489 | passivated with the $C_{12}$ ligands.  
489   \ref{fig:NP25_C12h1} shows one of the solvated 25 \AA\ nanoparticles
490   passivated with the $C_{12}$ ligands.  
491  
307 – \begin{figure}
308 –        \includegraphics[width=\linewidth]{figures/NP25_C12h1}
309 –        \caption{A 25 \AA\ radius gold nanoparticle protected with a
310 –          half-monolayer of TraPPE-UA dodecanethiolate (C$_{12}$)
311 –          ligands and solvated in TraPPE-UA hexane. The interfacial
312 –          thermal conductance is computed by applying a kinetic energy
313 –          flux between the nanoparticle and an outer shell of
314 –          solvent.}
315 –        \label{fig:NP25_C12h1}
316 – \end{figure}
317 –
492   Once equilibrated, thermal fluxes were applied for 1 ns, until stable
493   temperature gradients had developed. Systems were run under moderate
494   pressure (50 atm) with an average temperature (250K) that maintained a
# Line 352 | Line 526 | in order to sample multiple surface-ligand configurati
526   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
527   %               EFFECT OF PARTICLE SIZE
528   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
529 < \section{Results}
529 > \section*{Results}
530  
531   We modeled four sizes of nanoparticles ($R =$ 10, 15, 20, and 25
532   \AA). The smallest particle size produces the lowest interfacial
# Line 381 | Line 555 | nanoparticles.
555   increase in the interfacial thermal conductance over the bare
556   nanoparticles.
557  
384 – \begin{figure}
385 –        \includegraphics[width=\linewidth]{figures/NPthiols_G}
386 –        \caption{Interfacial thermal conductance ($G$) values for 4
387 –          sizes of solvated nanoparticles that are bare or protected
388 –          with a 50\% coverage of C$_{4}$, C$_{8}$, or C$_{12}$
389 –          alkanethiolate ligands.}
390 –        \label{fig:NPthiols_G}
391 – \end{figure}
392 –
558   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
559   %               HEAT TRANSFER MECHANISMS
560   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
561 < \section{Mechanisms for Ligand-Enhanced Heat Transfer}
561 > %\section*{Discussion}
562  
563   corrugation
564  
# Line 406 | Line 571 | orientation of solvent
571   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
572   %               CORRUGATION OF PARTICLE SURFACE
573   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
574 < \subsection{Corrugation of Particle Surface}
574 > \subsection*{Corrugation of Particle Surface}
575  
576   The bonding sites for thiols on gold surfaces have been studied
577   extensively and include configurations beyond the traditional atop,
# Line 467 | Line 632 | disruption of the lattice.
632   extends into the core of the nanoparticle, indicating widespread
633   disruption of the lattice.
634  
470 – \begin{figure}
471 –        \includegraphics[width=\linewidth]{figures/NP10_fcc}
472 –        \caption{Fraction of gold atoms with fcc ordering as a
473 –          function of radius for a 10 \AA\ radius nanoparticle. The
474 –          decreased fraction of fcc-ordered atoms in ligand-protected
475 –          nanoparticles relative to bare particles indicates
476 –          restructuring of the nanoparticle surface by the thiolate
477 –          sulfur atoms.}
478 –        \label{fig:Corrugation}
479 – \end{figure}
480 –
635   We may describe the thickness of the disrupted nanoparticle surface by
636   defining a corrugation factor, $c$, as the ratio of the radius at
637   which the fraction of gold atoms with fcc ordering is 0.9 and the
# Line 514 | Line 668 | at the interface when ligands are added.
668  
669  
670  
517 – \begin{figure}
518 –        \includegraphics[width=\linewidth]{figures/NPthiols_combo}
519 –        \caption{Computed corrugation values, solvent escape rates,
520 –          ligand orientational $P_2$ values, and interfacial solvent
521 –          orientational $P_2$ values for 4 sizes of solvated
522 –          nanoparticles that are bare or protected with a 50\%
523 –          coverage of C$_{4}$, C$_{8}$, or C$_{12}$ alkanethiolate
524 –          ligands.}
525 –        \label{fig:NPthiols_combo}
526 – \end{figure}
671  
528 –
672   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
673   %               MOBILITY OF INTERFACIAL SOLVENT
674   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
675 < \subsection{Mobility of Interfacial Solvent}
675 > \subsection*{Mobility of Interfacial Solvent}
676  
677   Another possible mechanism for increasing interfacial conductance is
678   the mobility of the interfacial solvent.  We used a survival
# Line 564 | Line 707 | ligands have significantly lower thermal conductance.
707   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
708   %               ORIENTATION OF LIGAND CHAINS
709   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
710 < \subsection{Orientation of Ligand Chains}
710 > \subsection*{Orientation of Ligand Chains}
711  
712   As the ligand chain length increases in length, it exhibits
713   significantly more conformational flexibility. Thus, different lengths
# Line 588 | Line 731 | population at $\cos{(\theta)} = 0$.
731   willing to lie down on the nanoparticle surface and exhibit increased
732   population at $\cos{(\theta)} = 0$.
733  
591 – \begin{figure}
592 –        \includegraphics[width=\linewidth]{figures/NP_pAngle}
593 –        \caption{The two extreme cases of ligand orientation relative
594 –          to the nanoparticle surface: the ligand completely
595 –          outstretched ($\cos{(\theta)} = -1$) and the ligand fully
596 –          lying down on the particle surface ($\cos{(\theta)} = 0$).}
597 –        \label{fig:NP_pAngle}
598 – \end{figure}
734  
735   % \begin{figure}
736   %       \includegraphics[width=\linewidth]{figures/thiol_pAngle}
# Line 620 | Line 755 | ligand chain length -- and ligand flexibility -- incre
755   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
756   %               ORIENTATION OF INTERFACIAL SOLVENT
757   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
758 < \subsection{Orientation of Interfacial Solvent}
758 > \subsection*{Orientation of Interfacial Solvent}
759  
760   Similarly, we examined the distribution of \emph{hexane} molecule
761   orientations relative to the particle surface using the same angular
# Line 663 | Line 798 | that lacks well-formed channels for the solvent molecu
798   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
799   %               SOLVENT PENETRATION OF LIGAND LAYER
800   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
801 < \subsection{Solvent Penetration of Ligand Layer}
801 > \subsection*{Solvent Penetration of Ligand Layer}
802  
803   We may also determine the extent of ligand -- solvent interaction by
804   calculating the hexane density as a function of radius. Figure
# Line 671 | Line 806 | and 50\% coverage of C$_{4}$, C$_{8}$, and C$_{12}$ th
806   profiles for a solvated 25 \AA\ radius nanoparticle with no ligands,
807   and 50\% coverage of C$_{4}$, C$_{8}$, and C$_{12}$ thiolates.
808  
674 – \begin{figure}
675 –        \includegraphics[width=\linewidth]{figures/hex_density}
676 –        \caption{Radial hexane density profiles for 25 \AA\ radius
677 –          nanoparticles with no ligands (circles), C$_{4}$ ligands
678 –          (squares), C$_{8}$ ligands (triangles), and C$_{12}$ ligands
679 –          (diamonds). As ligand chain length increases, the nearby
680 –          solvent is excluded from the ligand layer. Some solvent is
681 –          present inside the particle $r_{max}$ location due to
682 –          faceting of the nanoparticle surface.}
683 –        \label{fig:hex_density}
684 – \end{figure}
809  
810   The differences between the radii at which the hexane surrounding the
811   ligand-covered particles reaches bulk density correspond nearly
# Line 694 | Line 818 | the ligand layer as the chain length increases.
818   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
819   %               DISCUSSION
820   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
821 < \section{Discussion}
821 > \section*{Discussion}
822  
823   The chemical bond between the metal and the ligand introduces
824   vibrational overlap that is not present between the bare metal surface
# Line 712 | Line 836 | dramatically.
836   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
837   % **ACKNOWLEDGMENTS**
838   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
839 < \begin{acknowledgement}
839 > %\begin{acknowledgement}
840 > \section*{Acknowledgments}
841    Support for this project was provided by the National Science Foundation
842    under grant CHE-1362211. Computational time was provided by the
843    Center for Research Computing (CRC) at the University of Notre Dame.
844 < \end{acknowledgement}
844 > %\end{acknowledgement}
845  
846  
847 < \newpage
847 > %\section*{References}
848  
849 + \newpage
850   \bibliography{NPthiols}
851 + \newpage
852 + %\section*{Figure Legends}
853  
854 + \begin{figure}
855 +  \includegraphics[width=\linewidth]{figures/NP25_C12h1}
856 +  \caption{{\bf A 25 \AA\ radius gold nanoparticle protected with a
857 +      half-monolayer of TraPPE-UA dodecanethiolate (C$_{12}$)
858 +      ligands and solvated in TraPPE-UA hexane.} The interfacial
859 +    thermal conductance is computed by applying a kinetic energy
860 +    flux between the nanoparticle and an outer shell of
861 +    solvent.}
862 +  \label{fig:NP25_C12h1}
863 + \end{figure}
864 +
865 + \begin{figure}
866 +  \includegraphics[width=\linewidth]{figures/NPthiols_G}
867 +  \caption{{\bf Interfacial thermal conductance ($G$) values for 4
868 +      sizes of solvated nanoparticles that are bare or protected
869 +      with a 50\% coverage of C$_{4}$, C$_{8}$, or C$_{12}$
870 +      alkanethiolate ligands.}}
871 +  \label{fig:NPthiols_G}
872 + \end{figure}
873 +
874 + \begin{figure}
875 +  \includegraphics[width=\linewidth]{figures/NP10_fcc}
876 +  \caption{{\bf Fraction of gold atoms with fcc ordering as a
877 +      function of radius for a 10 \AA\ radius nanoparticle}. The
878 +    decreased fraction of fcc-ordered atoms in ligand-protected
879 +    nanoparticles relative to bare particles indicates
880 +    restructuring of the nanoparticle surface by the thiolate
881 +    sulfur atoms.}
882 +  \label{fig:Corrugation}
883 + \end{figure}
884 +
885 + \begin{figure}
886 +  \includegraphics[width=\linewidth]{figures/NPthiols_combo}
887 +  \caption{{\bf Computed corrugation values, solvent escape rates,
888 +      ligand orientational $P_2$ values, and interfacial solvent
889 +      orientational $P_2$ values for 4 sizes of solvated
890 +      nanoparticles that are bare or protected with a 50\%
891 +      coverage of C$_{4}$, C$_{8}$, or C$_{12}$ alkanethiolate
892 +      ligands.}}
893 +  \label{fig:NPthiols_combo}
894 + \end{figure}
895 +
896 + \begin{figure}
897 +  \includegraphics[width=\linewidth]{figures/NP_pAngle}
898 +  \caption{{\bf The two extreme cases of ligand orientation relative
899 +      to the nanoparticle surface: the ligand completely
900 +      outstretched ($\cos{(\theta)} = -1$) and the ligand fully
901 +      lying down on the particle surface ($\cos{(\theta)} = 0$).}}
902 +  \label{fig:NP_pAngle}
903 + \end{figure}
904 +
905 + \begin{figure}
906 +  \includegraphics[width=\linewidth]{figures/hex_density}
907 +  \caption{{\bf Radial hexane density profiles for 25 \AA\ radius
908 +      nanoparticles with no ligands (circles), C$_{4}$ ligands
909 +      (squares), C$_{8}$ ligands (triangles), and C$_{12}$ ligands
910 +      (diamonds).} As ligand chain length increases, the nearby
911 +    solvent is excluded from the ligand layer. Some solvent is
912 +    present inside the particle $r_{max}$ location due to
913 +    faceting of the nanoparticle surface.}
914 +  \label{fig:hex_density}
915 + \end{figure}
916 +
917   \end{document}

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