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\section{Introduction} |
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The structural and dynamical details of interfaces between metal |
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nanoparticles and solvents determines how energy flows between these |
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particles and their surroundings. Understanding this energy flow is |
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essential in designing and functionalizing metallic nanoparticles for |
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plasmonic photothermal |
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therapies,\cite{Jain:2007ux,Petrova:2007ad,Gnyawali:2008lp,Mazzaglia:2008to,Huff:2007ye,Larson:2007hw} which rely on the ability of metallic |
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nanoparticles to absorb light in the near-IR, a portion of the |
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spectrum in which living tissue is very nearly transparent. The |
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principle of this therapy is to pump the particles at high power at |
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the plasmon resonance and to allow heat dissipation to kill targeted |
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(e.g. cancerous) cells. The relevant physical property controlling |
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this transfer of energy is the interfacial thermal conductance, $G$, |
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which can be somewhat difficult to determine |
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experimentally.\cite{Wilson:2002uq,Plech:2005kx} |
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The structural details of the interfaces of metal nanoparticles |
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determines how energy flows between these particles and their |
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> |
surroundings. Understanding this energy flow is essential in designing |
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and functionalizing metallic nanoparticles for plasmonic photothermal |
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therapies,\cite{Jain:2007ux,Petrova:2007ad,Gnyawali:2008lp,Mazzaglia:2008to,Huff:2007ye,Larson:2007hw} |
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which rely on the ability of metallic nanoparticles to absorb light in |
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the near-IR, a portion of the spectrum in which living tissue is very |
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nearly transparent. The relevant physical property controlling the |
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transfer of this energy as heat into the surrounding tissue is the |
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interfacial thermal conductance, $G$, which can be somewhat difficult |
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to determine experimentally.\cite{Wilson:2002uq,Plech:2005kx} |
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Metallic particles have also been proposed for use in highly efficient |
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thermal-transfer fluids, although careful experiments by Eapen {\it et al.} |
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have shown that metal-particle-based ``nanofluids'' have thermal |
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conductivities that match Maxwell predictions.\cite{Eapen:2007th} The |
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likely cause of previously reported non-Maxwell |
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thermal-transfer fluids, although careful experiments by Eapen {\it et |
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al.} have shown that metal-particle-based ``nanofluids'' have |
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thermal conductivities that match Maxwell |
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predictions.\cite{Eapen:2007th} The likely cause of previously |
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reported non-Maxwell |
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behavior\cite{Eastman:2001wb,Keblinski:2002bx,Lee:1999ct,Xue:2003ya,Xue:2004oa} |
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is percolation networks of nanoparticles exchanging energy via the |
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solvent,\cite{Eapen:2007mw} so it is vital to get a detailed molecular |
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picture of particle-solvent interactions in order to understand the |
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thermal behavior of complex fluids. To date, there have been few |
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reported values (either from theory or experiment) for $G$ for |
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ligand-protected nanoparticles embedded in liquids, and there is a |
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significant gap in knowledge about how chemically distinct ligands or |
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protecting groups will affect heat transport from the particles. |
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picture of particle-ligand and particle-solvent interactions in order |
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to understand the thermal behavior of complex fluids. To date, there |
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have been few reported values (either from theory or experiment) for |
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$G$ for ligand-protected nanoparticles embedded in liquids, and there |
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is a significant gap in knowledge about how chemically distinct |
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ligands or protecting groups will affect heat transport from the |
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particles. |
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The thermal properties of various nanostructured interfaces have been |
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investigated experimentally by a number of groups: Cahill and |
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Experimentally, the thermal properties of various nanostructured |
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interfaces have been investigated by a number of groups. Cahill and |
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coworkers studied nanoscale thermal transport from metal |
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nanoparticle/fluid interfaces, to epitaxial TiN/single crystal oxides |
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nanoparticle/fluid interfaces, to epitaxial TiN/single crystal oxide |
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interfaces, and hydrophilic and hydrophobic interfaces between water |
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and solids with different self-assembled |
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monolayers.\cite{cahill:793,Wilson:2002uq,PhysRevB.67.054302,doi:10.1021/jp048375k,PhysRevLett.96.186101} |
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the vibrational spectra (metal to ligand, ligand to solvent) provides |
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a mechanism for rapid thermal transport across the interface. |
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One interesting result of our previous work was the observation of |
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{\it non-monotonic dependence} of the thermal conductance on the |
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coverage of a metal surface by a chemical protecting group. Our |
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explanation for this behavior was that gaps in surface coverage |
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allowed solvent to penetrate close to the capping molecules that had |
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been heated by the metal surface, to absorb thermal energy from these |
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molecules, and then diffuse away. The effect of surface coverage is |
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relatively difficult to study as the individual protecting groups have |
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lateral mobility on the surface and can aggregate to form domains on |
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the timescale of the simulation. |
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One notable result of our previous work was the observation of |
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non-monotonic dependence of the thermal conductance on the coverage of |
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a metal surface by a chemical protecting group. Our explanation for |
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this behavior was that gaps in surface coverage allowed solvent to |
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penetrate close to the capping molecules that had been heated by the |
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metal surface, to absorb thermal energy from these molecules, and then |
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diffuse away. The effect of surface coverage was relatively difficult |
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to study as the individual protecting groups have lateral mobility on |
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the surface and can aggregate to form domains on the timescale of the |
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simulation. |
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The work reported here involves the use of velocity shearing and |
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scaling reverse non-equilibrium molecular dynamics (VSS-RNEMD) to |
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study surfaces composed of mixed-length chains which collectively form |
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a complete monolayer on the surfaces. These complete (but |
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mixed-chain) surfaces are significantly less prone to surface domain |
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formation, and would allow us to further investigate the mechanism of |
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heat transport to the solvent. |
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To prevent lateral mobility of the surface ligands, the current work |
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involves mixed-chain monolayers in which the length mismatch between |
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long and short chains is sufficient to accomodate solvent |
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molecules. These complete (but mixed-chain) surfaces are significantly |
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less prone to surface domain formation, and allow us to further |
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investigate the mechanism of heat transport to the solvent. A thermal |
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flux is created using velocity shearing and scaling reverse |
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non-equilibrium molecular dynamics (VSS-RNEMD), and the resulting |
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temperature profiles are analyzed to yield information about the |
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interfacial thermal conductance. |
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+ |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% **METHODOLOGY** |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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undesirable side-effects when the applied flux becomes |
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large.\cite{Maginn:2010} |
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|
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Instead of having momentum exchange between {\it individual particles} |
| 209 |
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in each slab, the NIVS algorithm applies velocity scaling to all of |
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the selected particles in both slabs.\cite{Kuang:2010uq} A combination |
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of linear momentum, kinetic energy, and flux constraint equations |
| 209 |
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governs the amount of velocity scaling performed at each step. NIVS |
| 210 |
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has been shown to be very effective at producing thermal gradients and |
| 211 |
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for computing thermal conductivities, particularly for heterogeneous |
| 212 |
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interfaces. Although the NIVS algorithm can also be applied to impose |
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< |
a directional momentum flux, thermal anisotropy was observed in |
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relatively high flux simulations, and the method is not suitable for |
| 215 |
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imposing a shear flux or for computing shear viscosities. |
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|
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The most useful RNEMD |
| 218 |
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approach developed so far utilizes a series of simultaneous velocity |
| 219 |
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shearing and scaling exchanges between the two |
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slabs.\cite{2012MolPh.110..691K} This method provides a set of |
| 208 |
> |
The most useful alternative RNEMD approach developed so far utilizes a |
| 209 |
> |
series of simultaneous velocity shearing and scaling exchanges between |
| 210 |
> |
the two slabs.\cite{2012MolPh.110..691K} This method provides a set of |
| 211 |
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conservation constraints while simultaneously creating a desired flux |
| 212 |
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between the two slabs. Satisfying the constraint equations ensures |
| 213 |
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that the new configurations are sampled from the same NVE ensemble. |
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kept to a minimum. This ability to generate simultaneous thermal and |
| 287 |
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shear fluxes has been previously utilized to map out the shear |
| 288 |
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viscosity of SPC/E water over a wide range of temperatures (90~K) with |
| 289 |
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a {\it single 1 ns simulation}.\cite{2012MolPh.110..691K} |
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a single 1 ns simulation.\cite{2012MolPh.110..691K} |
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|
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\begin{figure} |
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\includegraphics[width=\linewidth]{figures/rnemd} |