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\usepackage[version=3]{mhchem} % this is a great package for formatting chemical reactions |
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\usepackage{url} |
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\title{Simulations of Interfacial Thermal Conductance of Alkanethiolate Ligand-Protected Gold Nanoparticles} |
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\title{The Thermal Conductance of Alkanethiolate-Protected Gold |
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Nanospheres: Effects of Curvature and Chain Length} |
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\author{Kelsey M. Stocker} |
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\author{J. Daniel Gezelter} |
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The thermal properties of various nanostructured interfaces have been |
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the subject of intense experimental |
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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} |
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The interfacial thermal conductance ($G$) is the principal quantity of |
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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} |
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and the interfacial thermal conductance is the principal quantity of |
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interest for understanding interfacial heat |
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transport.\cite{cahill:793} Nanoparticles have a significant fraction |
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of their atoms at interfaces, and the chemical details of these |
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interfaces govern the thermal transport properties. |
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transport.\cite{cahill:793} Because nanoparticles have a significant |
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fraction of their atoms at the particle / solvent interface, the |
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chemical details of these interfaces govern the thermal transport |
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properties. |
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Previously, reverse non-equilibrium molecular dynamics (RNEMD) methods |
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have been applied to calculate the interfacial thermal conductance at |
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metal / organic solvent interfaces that had been chemically protected |
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by mixed-chain alkanethiolate groups.\cite{kuang:AuThl} These |
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simulations suggest an explanation for the very large thermal |
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conductivity at alkanethiol-capped metal surfaces. Specifically, the |
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chemical bond between the metal and the ligand introduces a |
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vibrational overlap that is not present without the protecting group, |
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and the overlap between the vibrational spectra (metal to ligand, |
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ligand to solvent) provides a mechanism for rapid thermal transport |
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across the interface. The simulations also suggest that this |
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phenomenon is a non-monotonic function of the fractional coverage of |
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the surface, as moderate coverages allow diffusive heat transport of |
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solvent molecules that have been in close contact with the ligands. |
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flat (111) metal / organic solvent interfaces that had been chemically |
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protected by mixed-chain alkanethiolate groups.\cite{kuang:AuThl} |
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These simulations suggested an explanation for the increase in thermal |
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conductivity at alkanethiol-capped metal surfaces compared with bare |
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metal interfaces. Specifically, the chemical bond between the metal |
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and the ligand introduces a vibrational overlap that is not present |
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without the protecting group, and the overlap between the vibrational |
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spectra (metal to ligand, ligand to solvent) provides a mechanism for |
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rapid thermal transport across the interface. The simulations also |
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suggest that this phenomenon is a non-monotonic function of the |
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fractional coverage of the surface, as moderate coverages allow |
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diffusive heat transport of solvent molecules that have been in close |
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contact with the ligands. |
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Additionally, simulations of {\it mixed-chain} alkylthiolate surfaces |
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showed that entrapped solvent can be very efficient at moving thermal |
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energy away from the surface.\cite{Stocker2013} Trapped solvent that |
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energy away from the surface.\cite{Stocker:2013cl} Trapped solvent that |
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is orientationally coupled to the ordered ligands (and is less able to |
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diffuse into the bulk) were able to double the thermal conductance of |
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the interface. |
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\end{equation} |
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which depends on the solvent heat capacity, $C_s$, solvent thermal |
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conductivity, $\Lambda_s$, particle radius, $R$, and nanoparticle heat |
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capacity, $C_p$.\cite{Wilson:2002uq} In the infinite interfacial |
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thermal conductance limit $G >> G_c$, the particle cooling rate is |
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limited by the solvent properties, $C_s$ and $\Lambda_s$. In the |
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opposite limit ($G << G_c$), the heat dissipation is controlled by the |
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thermal conductance of the particle / fluid interface. It is this |
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regime with which we are concerned, where properties of the interface |
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may be tuned to manipulate the rate of cooling for a solvated |
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nanoparticle. Based on $G$ values from previous simulations of gold |
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nanoparticles solvated in hexane and experimental results for solvated |
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nanostructures, it appears that we are in the $G << G_c$ regime for |
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gold nanoparticles of radius $< 400$ \AA\ solvated in hexane. The |
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particles included in this study are more than an order of magnitude |
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smaller than this critical radius. The heat dissipation should thus be |
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controlled entirely by the surface features of the particle / ligand / |
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solvent interface. |
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capacity, $C_p$.\cite{Wilson:2002uq} In the limit of infinite |
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interfacial thermal conductance, $G >> G_c$, cooling of the |
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nanoparticle is limited by the solvent properties, $C_s$ and |
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$\Lambda_s$. In the opposite limit ($G << G_c$), the heat dissipation |
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is controlled by the thermal conductance of the particle / fluid |
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interface. It is this regime with which we are concerned, where |
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properties of the interface may be tuned to manipulate the rate of |
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cooling for a solvated nanoparticle. Based on estimates of $G$ from |
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previous simulations of gold nanoparticles solvated in hexane and |
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experimental results for solvated nanostructures, it appears that we |
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are in the $G << G_c$ regime for gold nanoparticles with radii smaller |
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than 40 nm when solvated in hexane. The particles included in this |
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study are more than an order of magnitude smaller than this critical |
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radius, so the heat dissipation should be controlled entirely by the |
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surface features of the particle / ligand / solvent interface. |
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% 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} |
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% |
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We use a survival correlation function, $C(t)$, to measure the |
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residence time of a solvent molecule in the nanoparticle thiolate |
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layer.\cite{Stocker2013} This function correlates the identity of all |
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layer.\cite{Stocker:2013cl} This function correlates the identity of all |
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hexane molecules within the radial range of the thiolate layer at two |
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separate times. If the solvent molecule is present at both times, the |
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configuration contributes a $1$, while the absence of the molecule at |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\begin{acknowledgement} |
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Support for this project was provided by the National Science Foundation |
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under grant CHE-0848243. Computational time was provided by the |
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under grant CHE-1362211. Computational time was provided by the |
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Center for Research Computing (CRC) at the University of Notre Dame. |
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\end{acknowledgement} |
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