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Revision 4131 by kstocke1, Wed May 21 19:45:22 2014 UTC vs.
Revision 4146 by gezelter, Thu May 22 15:47:19 2014 UTC

# Line 1 | Line 1
1 < \documentclass[journal = jctcce, manuscript = article]{achemso}
1 > \documentclass[journal = jpccck, manuscript = article]{achemso}
2   \setkeys{acs}{usetitle = true}
3  
4   \usepackage{caption}
# Line 25 | Line 25
25   \author{Kelsey M. Stocker}
26   \author{J. Daniel Gezelter}
27   \email{gezelter@nd.edu}
28 < \affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\ Department of Chemistry and Biochemistry\\ University of Notre Dame\\ Notre Dame, Indiana 46556}
28 > \affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\
29 > Department of Chemistry and Biochemistry\\
30 > University of Notre Dame\\
31 > Notre Dame, Indiana 46556}
32  
33 +
34 + \keywords{Nanoparticles, interfaces, thermal conductance}
35 +
36   \begin{document}
37  
38   \begin{tocentry}
# Line 36 | Line 42
42   \newcolumntype{A}{p{1.5in}}
43   \newcolumntype{B}{p{0.75in}}
44  
39 – % \author{Kelsey M. Stocker and J. Daniel
40 – %   Gezelter\footnote{Corresponding author. \ Electronic mail:
41 – %     gezelter@nd.edu} \\
42 – %   251 Nieuwland Science Hall, \\
43 – %       Department of Chemistry and Biochemistry,\\
44 – %       University of Notre Dame\\
45 – %       Notre Dame, Indiana 46556}
45  
47 – %\date{\today}
48 –
49 – %\maketitle
50 –
51 – %\begin{doublespace}
52 –
46   \begin{abstract}
47          
48   \end{abstract}
# Line 61 | Line 54
54   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
55   \section{Introduction}
56  
57 + The thermal properties of various nanostructured interfaces have been
58 + the subject of intense experimental
59 + interest.\cite{Wilson:2002uq,PhysRevB.67.054302,doi:10.1021/jp048375k,PhysRevLett.96.186101,Wang10082007,doi:10.1021/jp8051888,PhysRevB.80.195406,doi:10.1021/la904855s}
60 + The interfacial thermal conductance ($G$) is the principal quantity of
61 + interest for understanding interfacial heat
62 + transport.\cite{cahill:793} Nanoparticles have a significant fraction
63 + of their atoms at interfaces, and the chemical details of these
64 + interfaces govern the thermal transport properties.
65 +
66 + Previously, reverse non-equilibrium molecular dynamics (RNEMD) methods
67 + have been applied to calculate the interfacial thermal conductance at
68 + metal / organic solvent interfaces that had been chemically protected
69 + by mixed-chain alkanethiolate groups.\cite{kuang:AuThl} These
70 + simulations suggest an explanation for the very large thermal
71 + conductivity at alkanethiol-capped metal surfaces.  Specifically, the
72 + chemical bond between the metal and the ligand introduces a
73 + vibrational overlap that is not present without the protecting group,
74 + and the overlap between the vibrational spectra (metal to ligand,
75 + ligand to solvent) provides a mechanism for rapid thermal transport
76 + across the interface. The simulations also suggest that this
77 + phenomenon is a non-monotonic function of the fractional coverage of
78 + the surface, as moderate coverages allow diffusive heat transport of
79 + solvent molecules that have been in close contact with the ligands.
80 +
81 + Additionally, simulations of {\it mixed-chain} alkylthiolate surfaces
82 + showed that entrapped solvent can be very efficient at moving thermal
83 + energy away from the surface.\cite{Stocker2013} Trapped solvent that
84 + is orientationally coupled to the ordered ligands (and is less able to
85 + diffuse into the bulk) were able to double the thermal conductance of
86 + the interface.
87 +
88 + Recently, we extended RNEMD methods for use in non-periodic geometries
89 + by creating scaling/shearing moves between concentric regions of the
90 + simulation.\cite{Stocker:2014qq} The primary reason for developing a
91 + non-periodic variant of RNEMD is to investigate the role that {\it
92 +  curved} nanoparticle surfaces play in heat and mass transport.  On
93 + planar surfaces, we discovered that orientational ordering of surface
94 + protecting ligands had a large effect on the heat conduction from the
95 + metal to the solvent.  Smaller nanoparticles have high surface
96 + curvature that creates gaps in well-ordered self-assembled monolayers,
97 + and the effect those gaps will have on the thermal conductance are
98 + unknown.
99 +
100 +
101 +
102   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
103   %               INTERFACIAL THERMAL CONDUCTANCE OF METALLIC NANOPARTICLES
104   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
105 < \section{Interfacial Thermal Conductance of Metallic Nanoparticles}
105 > %\section{Interfacial Thermal Conductance of Metallic Nanoparticles}
106  
107 < For a solvated nanoparticle, we can define a critical interfacial thermal conductance value,
107 > For a solvated nanoparticle, we can define a critical value for the
108 > interfacial thermal conductance,
109   \begin{equation}
110 < G_c = \frac{3 C_f \Lambda_f}{r C_p}
110 > G_c = \frac{3 C_s \Lambda_s}{R C_p}
111   \end{equation}
112 + which depends on the solvent heat capacity, $C_s$, solvent thermal
113 + conductivity, $\Lambda_s$, particle radius, $R$, and nanoparticle heat
114 + capacity, $C_p$.\cite{Wilson:2002uq} In the infinite interfacial
115 + thermal conductance limit $G >> G_c$, the particle cooling rate is
116 + limited by the solvent properties, $C_s$ and $\Lambda_s$. In the
117 + opposite limit ($G << G_c$), the heat dissipation is controlled by the
118 + thermal conductance of the particle / fluid interface. It is this
119 + regime with which we are concerned, where properties of the interface
120 + may be tuned to manipulate the rate of cooling for a solvated
121 + nanoparticle. Based on $G$ values from previous simulations of gold
122 + nanoparticles solvated in hexane and experimental results for solvated
123 + nanostructures, it appears that we are in the $G << G_c$ regime for
124 + gold nanoparticles of radius $< 400$ \AA\ solvated in hexane. The
125 + particles included in this study are more than an order of magnitude
126 + smaller than this critical radius. The heat dissipation should thus be
127 + controlled entirely by the surface features of the particle / ligand /
128 + solvent interface.
129  
74 – dependent upon the fluid heat capacity, $C_f$, fluid thermal conductivity, $\Lambda_f$, particle radius, $r$, and nanoparticle heat capacity, $C_p$.\cite{Wilson:2002uq} In the infinite interfacial thermal conductance limit $G >> G_c$, the particle cooling rate is limited by the fluid properties, $C_f$ and $\Lambda_f$. In the opposite limit ($G << G_c$), the heat dissipation is controlled by the thermal conductance of the particle / fluid interface. It is this regime with which we are concerned, where properties of the interface may be tuned to manipulate the rate of cooling for a solvated nanoparticle. Based on $G$ values from previous simulations of gold nanoparticles solvated in hexane and experimental results for solvated nanostructures, it appears that we are in the $G << G_c$ regime for gold nanoparticles of radius $<$ 400 \AA\ solvated in hexane. The particles included in this study are more than an order of magnitude smaller than this critical radius. The heat dissipation should thus be controlled entirely by the surface features of the particle / ligand / solvent interface.
75 –
130   % Understanding how the structural details of the interfaces affect the energy flow between the particle and its surroundings is essential in designing and functionalizing metallic nanoparticles for use in plasmonic photothermal therapies,\cite{Jain:2007ux,Petrova:2007ad,Gnyawali:2008lp,Mazzaglia:2008to,Huff:2007ye,Larson:2007hw} which rely on the ability of metallic nanoparticles to absorb light in the near-IR, a portion of the spectrum in which living tissue is very nearly transparent. The relevant physical property controlling the transfer of this energy as heat into the surrounding tissue is the interfacial thermal conductance, $G$, which can be somewhat difficult to determine experimentally.\cite{Wilson:2002uq,Plech:2005kx}
131   %
132   % Metallic particles have also been proposed for use in efficient thermal-transfer fluids, although careful experiments by Eapen \textit{et al.} have shown that metal-particle-based nanofluids have thermal conductivities that match Maxwell predictions.\cite{Eapen:2007th} The likely cause of previously reported non-Maxwell behavior\cite{Eastman:2001wb,Keblinski:2002bx,Lee:1999ct,Xue:2003ya,Xue:2004oa} is percolation networks of nanoparticles exchanging energy via the solvent,\cite{Eapen:2007mw} so it is important to get a detailed molecular picture of particle-ligand and ligand-solvent interactions in order to understand the thermal behavior of complex fluids. To date, there have been some reported values from experiment\cite{Wilson:2002uq,doi:10.1021jp8051888,doi:10.1021jp048375k,Ge2005,Park2012}) of $G$ for ligand-protected nanoparticles embedded in liquids, but there is still a significant gap in knowledge about how chemically distinct ligands or protecting groups will affect heat transport from the particles. In particular, the dearth of atomistic, dynamic information available from molecular dynamics simulations means that the heat transfer mechanisms at these nanoparticle surfaces remain largely unclear.
# Line 82 | Line 136 | Though the ligand packing on planar surfaces is charac
136   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
137   \section{Structure of Self-Assembled Monolayers on Nanoparticles}
138  
139 < Though the ligand packing on planar surfaces is characterized for many different ligands and surface facets, it is not obvious \emph{a priori} how the same ligands will behave on the highly curved surfaces of nanoparticles. Thus, as more applications of ligand-stabilized nanostructures have become apparent, the structure and dynamics of ligands on metallic nanoparticles have been studied extensively.\cite{Badia1996:2,Badia1996,Henz2007,Badia1997:2,Badia1997,Badia2000} Badia, \textit{et al.} used transmission electron microscopy to determine that alkanethiol ligands on gold nanoparticles pack approximately 30\% more densely than on planar Au(111) surfaces.\cite{Badia1996:2} Subsequent experiments demonstrated that even at full coverages, surface curvature creates voids between linear ligand chains that can be filled via interdigitation of ligands on neighboring particles.\cite{Badia1996} The molecular dynamics simulations of Henz, \textit{et al.} indicate that at low coverages, the thiolate alkane chains will lie flat on the nanoparticle surface\cite{Henz2007} Above 90\% coverage, the ligands stand upright and recover the rigidity and tilt angle displayed on planar facets. Their simulations also indicate a high degree of mixing between the thiolate sulfur atoms and surface gold atoms at high coverages.
139 > Though the ligand packing on planar surfaces is characterized for many
140 > different ligands and surface facets, it is not obvious \emph{a
141 >  priori} how the same ligands will behave on the highly curved
142 > surfaces of nanoparticles. Thus, as more applications of
143 > ligand-stabilized nanostructures have become apparent, the structure
144 > and dynamics of ligands on metallic nanoparticles have been studied
145 > extensively.\cite{Badia1996:2,Badia1996,Henz2007,Badia1997:2,Badia1997,Badia2000}
146 > Badia, \textit{et al.} used transmission electron microscopy to
147 > determine that alkanethiol ligands on gold nanoparticles pack
148 > approximately 30\% more densely than on planar Au(111)
149 > surfaces.\cite{Badia1996:2} Subsequent experiments demonstrated that
150 > even at full coverages, surface curvature creates voids between linear
151 > ligand chains that can be filled via interdigitation of ligands on
152 > neighboring particles.\cite{Badia1996} The molecular dynamics
153 > simulations of Henz, \textit{et al.} indicate that at low coverages,
154 > the thiolate alkane chains will lie flat on the nanoparticle
155 > surface\cite{Henz2007} Above 90\% coverage, the ligands stand upright
156 > and recover the rigidity and tilt angle displayed on planar
157 > facets. Their simulations also indicate a high degree of mixing
158 > between the thiolate sulfur atoms and surface gold atoms at high
159 > coverages.
160  
161   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
162   %               NON-PERIODIC VSS-RNEMD METHODOLOGY
163   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
164   \section{Non-Periodic Velocity Shearing and Scaling RNEMD Methodology}
165  
166 < Non-periodic VSS-RNEMD, explained in detail in Chapter 4, periodically applies a series of velocity scaling and shearing moves at regular intervals to impose a flux between two concentric spherical regions.
166 > Non-periodic VSS-RNEMD,\cite{Stocker:2014qq} periodically applies a
167 > series of velocity scaling and shearing moves at regular intervals to
168 > impose a flux between two concentric spherical regions.
169  
170   To simultaneously impose a thermal flux ($J_r$) between the shells we
171   use energy conservation constraints,
# Line 118 | Line 194 | As described in Chapter 4, we can describe the thermal
194   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
195   \subsection{Interfacial Thermal Conductance}
196  
197 < As described in Chapter 4, we can describe the thermal conductance of each spherical shell as the inverse Kapitza resistance. To describe the thermal conductance for an interface of considerable thickness, such as the ligand layers shown here, we can sum the individual thermal resistances of each concentric spherical shell to arrive at the total thermal resistance, or the inverse of the total interfacial thermal conductance:
197 > We can describe the thermal conductance of each spherical shell as the
198 > inverse Kapitza resistance. To describe the thermal conductance for an
199 > interface of considerable thickness, such as the ligand layers shown
200 > here, we can sum the individual thermal resistances of each concentric
201 > spherical shell to arrive at the total thermal resistance, or the
202 > inverse of the total interfacial thermal conductance:
203  
204   \begin{equation}
205    \frac{1}{G} = R_\mathrm{total} = \frac{1}{q_r} \sum_i \left(T_{i+i} -
# Line 255 | Line 336 | As in the planar case described in Chapter 3, I use a
336   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
337   \subsection{Mobility of Interfacial Solvent}
338  
339 < As in the planar case described in Chapter 3, I use a survival correlation function, $C(t)$, to measure the residence time of a solvent molecule in the nanoparticle thiolate layer. This function correlates the identity of all hexane molecules within the radial range of the thiolate layer at two separate times. If the solvent molecule is present at both times, the configuration contributes a $1$, while the absence of the molecule at the later time indicates that the solvent molecule has migrated into the bulk, and this configuration contributes a $0$. A steep decay in $C(t)$ indicates a high turnover rate of solvent molecules from the chain region to the bulk. We may define the escape rate for trapped solvent molecules at the interface as
339 > We use a survival correlation function, $C(t)$, to measure the
340 > residence time of a solvent molecule in the nanoparticle thiolate
341 > layer.\cite{Stocker2013} This function correlates the identity of all
342 > hexane molecules within the radial range of the thiolate layer at two
343 > separate times. If the solvent molecule is present at both times, the
344 > configuration contributes a $1$, while the absence of the molecule at
345 > the later time indicates that the solvent molecule has migrated into
346 > the bulk, and this configuration contributes a $0$. A steep decay in
347 > $C(t)$ indicates a high turnover rate of solvent molecules from the
348 > chain region to the bulk. We may define the escape rate for trapped
349 > solvent molecules at the interface as
350  
351   \begin{equation}
352   k_{escape} = \left( \int_0^T C(t) dt \right)^{-1}
# Line 354 | Line 445 | The heat transfer mechanisms proposed in Chapter 3 can
445  
446   \bibliography{NPthiols}
447  
448 < \end{document}
448 > \end{document}

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