| 59 |
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|
| 60 |
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The intro. |
| 61 |
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|
| 62 |
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\section{Methodology} |
| 63 |
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\subsection{Algorithm} |
| 64 |
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There have been many algorithms for computing thermal conductivity |
| 65 |
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using molecular dynamics simulations. However, interfacial conductance |
| 66 |
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is at least an order of magnitude smaller. This would make the |
| 67 |
+ |
calculation even more difficult for those slowly-converging |
| 68 |
+ |
equilibrium methods. Imposed-flux non-equilibrium |
| 69 |
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methods\cite{MullerPlathe:1997xw} have the flux set {\it a priori} and |
| 70 |
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the response of temperature or momentum gradients are easier to |
| 71 |
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measure than the flux, if unknown, and thus, is a preferable way to |
| 72 |
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the forward NEMD methods. Although the momentum swapping approach for |
| 73 |
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flux-imposing can be used for exchanging energy between particles of |
| 74 |
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different identity, the kinetic energy transfer efficiency is affected |
| 75 |
+ |
by the mass difference between the particles, which limits its |
| 76 |
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application on heterogeneous interfacial systems. |
| 77 |
+ |
|
| 78 |
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The non-isotropic velocity scaling (NIVS)\cite{kuang:164101} approach in |
| 79 |
+ |
non-equilibrium MD simulations is able to impose relatively large |
| 80 |
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kinetic energy flux without obvious perturbation to the velocity |
| 81 |
+ |
distribution of the simulated systems. Furthermore, this approach has |
| 82 |
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the advantage in heterogeneous interfaces in that kinetic energy flux |
| 83 |
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can be applied between regions of particles of arbitary identity, and |
| 84 |
+ |
the flux quantity is not restricted by particle mass difference. |
| 85 |
+ |
|
| 86 |
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The NIVS algorithm scales the velocity vectors in two separate regions |
| 87 |
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of a simulation system with respective diagonal scaling matricies. To |
| 88 |
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determine these scaling factors in the matricies, a set of equations |
| 89 |
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including linear momentum conservation and kinetic energy conservation |
| 90 |
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constraints and target momentum/energy flux satisfaction is |
| 91 |
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solved. With the scaling operation applied to the system in a set |
| 92 |
+ |
frequency, corresponding momentum/temperature gradients can be built, |
| 93 |
+ |
which can be used for computing transportation properties and other |
| 94 |
+ |
applications related to momentum/temperature gradients. The NIVS |
| 95 |
+ |
algorithm conserves momenta and energy and does not depend on an |
| 96 |
+ |
external thermostat. |
| 97 |
+ |
|
| 98 |
+ |
(wondering how much detail of algorithm should be put here...) |
| 99 |
+ |
|
| 100 |
+ |
\subsection{Simulation Parameters} |
| 101 |
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Our simulation systems consists of metal gold lattice slab solvated by |
| 102 |
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organic solvents. In order to study the role of capping agents in |
| 103 |
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interfacial thermal conductance, butanethiol is chosen to cover gold |
| 104 |
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surfaces in comparison to no capping agent present. |
| 105 |
+ |
|
| 106 |
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The Au-Au interactions in metal lattice slab is described by the |
| 107 |
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quantum Sutton-Chen (QSC) formulation.\cite{PhysRevB.59.3527} The QSC |
| 108 |
+ |
potentials include zero-point quantum corrections and are |
| 109 |
+ |
reparametrized for accurate surface energies compared to the |
| 110 |
+ |
Sutton-Chen potentials\cite{Chen90}. |
| 111 |
+ |
|
| 112 |
+ |
Straight chain {\it n}-hexane and aromatic toluene are respectively |
| 113 |
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used as solvents. For hexane, both United-Atom\cite{TraPPE-UA.alkanes} |
| 114 |
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and All-Atom\cite{OPLSAA} force fields are used for comparison; for |
| 115 |
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toluene, United-Atom\cite{TraPPE-UA.alkylbenzenes} force fields are |
| 116 |
+ |
used with rigid body constraints applied. (maybe needs more details |
| 117 |
+ |
about rigid body) |
| 118 |
+ |
|
| 119 |
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Buatnethiol molecules are used as capping agent for some of our |
| 120 |
+ |
simulations. United-Atom\cite{TraPPE-UA.thiols} and All-Atom models |
| 121 |
+ |
are respectively used corresponding to the force field type of |
| 122 |
+ |
solvent. |
| 123 |
+ |
|
| 124 |
+ |
To describe the interactions between metal Au and non-metal capping |
| 125 |
+ |
agent and solvent, we refer to Vlugt\cite{vlugt:cpc2007154} and derive |
| 126 |
+ |
other interactions which are not parametrized in their work. (can add |
| 127 |
+ |
hautman and klein's paper here and more discussion; need to put |
| 128 |
+ |
aromatic-metal interaction approximation here) |
| 129 |
+ |
|
| 130 |
+ |
\section{Computational Details} |
| 131 |
+ |
Our simulation systems consists of a lattice Au slab with the (111) |
| 132 |
+ |
surface perpendicular to the $z$-axis, and a solvent layer between the |
| 133 |
+ |
periodic Au slabs along the $z$-axis. To set up the interfacial |
| 134 |
+ |
system, the Au slab is first equilibrated without solvent under room |
| 135 |
+ |
pressure and a desired temperature. After the metal slab is |
| 136 |
+ |
equilibrated, United-Atom or All-Atom butanethiols are replicated on |
| 137 |
+ |
the Au surface, each occupying the (??) among three Au atoms, and is |
| 138 |
+ |
equilibrated under NVT ensemble. According to (CITATION), the maximal |
| 139 |
+ |
thiol capacity on Au surface is $1/3$ of the total number of surface |
| 140 |
+ |
Au atoms. |
| 141 |
+ |
|
| 142 |
+ |
\cite{packmol} |
| 143 |
+ |
|
| 144 |
|
\section{Acknowledgments} |
| 145 |
|
Support for this project was provided by the National Science |
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|
Foundation under grant CHE-0848243. Computational time was provided by |
