[ViewVC] Diff of: group/interfacial/interfacial.tex

Comparing interfacial/interfacial.tex (file contents):
Revision 3717 by gezelter, Thu Jan 27 16:29:20 2011 UTC vs.
Revision 3725 by skuang, Mon May 9 19:08:08 2011 UTC

+\begin{doublespace}
+\begin{abstract}
-<
+The abstract
->
->
+We have developed a Non-Isotropic Velocity Scaling algorithm for
->
+setting up and maintaining stable thermal gradients in non-equilibrium
->
+molecular dynamics simulations. This approach effectively imposes
->
+unphysical thermal flux even between particles of different
->
+identities, conserves linear momentum and kinetic energy, and
->
+minimally perturbs the velocity profile of a system when compared with
->
+previous RNEMD methods. We have used this method to simulate thermal
->
+conductance at metal / organic solvent interfaces both with and
->
+without the presence of thiol-based capping agents.  We obtained
->
+values comparable with experimental values, and observed significant
->
+conductance enhancement with the presence of capping agents. Computed
->
+power spectra indicate the acoustic impedance mismatch between metal
->
+and liquid phase is greatly reduced by the capping agents and thus
->
+leads to higher interfacial thermal transfer efficiency.
->
+\end{abstract}
+\newpage
+\section{Introduction}
-<
+The intro.
->
+Interfacial thermal conductance is extensively studied both
->
+experimentally and computationally, and systems with interfaces
->
+present are generally heterogeneous. Although interfaces are commonly
->
+barriers to heat transfer, it has been
->
+reported\cite{doi:10.1021/la904855s} that under specific circustances,
->
+e.g. with certain capping agents present on the surface, interfacial
->
+conductance can be significantly enhanced. However, heat conductance
->
+of molecular and nano-scale interfaces will be affected by the
->
+chemical details of the surface and is challenging to
->
+experimentalist. The lower thermal flux through interfaces is even
->
+more difficult to measure with EMD and forward NEMD simulation
->
+methods. Therefore, developing good simulation methods will be
->
+desirable in order to investigate thermal transport across interfaces.
-+
+Recently, we have developed the Non-Isotropic Velocity Scaling (NIVS)
-+
+algorithm for RNEMD simulations\cite{kuang:164101}. This algorithm
-+
+retains the desirable features of RNEMD (conservation of linear
-+
+momentum and total energy, compatibility with periodic boundary
-+
+conditions) while establishing true thermal distributions in each of
-+
+the two slabs. Furthermore, it allows more effective thermal exchange
-+
+between particles of different identities, and thus enables extensive
-+
+study of interfacial conductance.
-+
-+
+\section{Methodology}
-+
+\subsection{Algorithm}
-+
+There have been many algorithms for computing thermal conductivity
-+
+using molecular dynamics simulations. However, interfacial conductance
-+
+is at least an order of magnitude smaller. This would make the
-+
+calculation even more difficult for those slowly-converging
-+
+equilibrium methods. Imposed-flux non-equilibrium
-+
+methods\cite{MullerPlathe:1997xw} have the flux set {\it a priori} and
-+
+the response of temperature or momentum gradients are easier to
-+
+measure than the flux, if unknown, and thus, is a preferable way to
-+
+the forward NEMD methods. Although the momentum swapping approach for
-+
+flux-imposing can be used for exchanging energy between particles of
-+
+different identity, the kinetic energy transfer efficiency is affected
-+
+by the mass difference between the particles, which limits its
-+
+application on heterogeneous interfacial systems.
-+
-+
+The non-isotropic velocity scaling (NIVS)\cite{kuang:164101} approach in
-+
+non-equilibrium MD simulations is able to impose relatively large
-+
+kinetic energy flux without obvious perturbation to the velocity
-+
+distribution of the simulated systems. Furthermore, this approach has
-+
+the advantage in heterogeneous interfaces in that kinetic energy flux
-+
+can be applied between regions of particles of arbitary identity, and
-+
+the flux quantity is not restricted by particle mass difference.
-+
-+
+The NIVS algorithm scales the velocity vectors in two separate regions
-+
+of a simulation system with respective diagonal scaling matricies. To
-+
+determine these scaling factors in the matricies, a set of equations
-+
+including linear momentum conservation and kinetic energy conservation
-+
+constraints and target momentum/energy flux satisfaction is
-+
+solved. With the scaling operation applied to the system in a set
-+
+frequency, corresponding momentum/temperature gradients can be built,
-+
+which can be used for computing transportation properties and other
-+
+applications related to momentum/temperature gradients. The NIVS
-+
+algorithm conserves momenta and energy and does not depend on an
-+
+external thermostat.
-+
-+
+(wondering how much detail of algorithm should be put here...)
-+
-+
+\subsection{Force Field Parameters}
-+
+Our simulation systems consists of metal gold lattice slab solvated by
-+
+organic solvents. In order to study the role of capping agents in
-+
+interfacial thermal conductance, butanethiol is chosen to cover gold
-+
+surfaces in comparison to no capping agent present.
-+
-+
+The Au-Au interactions in metal lattice slab is described by the
-+
+quantum Sutton-Chen (QSC) formulation.\cite{PhysRevB.59.3527} The QSC
-+
+potentials include zero-point quantum corrections and are
-+
+reparametrized for accurate surface energies compared to the
-+
+Sutton-Chen potentials\cite{Chen90}.
-+
-+
+Straight chain {\it n}-hexane and aromatic toluene are respectively
-+
+used as solvents. For hexane, both United-Atom\cite{TraPPE-UA.alkanes}
-+
+and All-Atom\cite{OPLSAA} force fields are used for comparison; for
-+
+toluene, United-Atom\cite{TraPPE-UA.alkylbenzenes} force fields are
-+
+used with rigid body constraints applied. (maybe needs more details
-+
+about rigid body)
-+
-+
+Buatnethiol molecules are used as capping agent for some of our
-+
+simulations. United-Atom\cite{TraPPE-UA.thiols} and All-Atom models
-+
+are respectively used corresponding to the force field type of
-+
+solvent.
-+
-+
+To describe the interactions between metal Au and non-metal capping
-+
+agent and solvent, we refer to Vlugt\cite{vlugt:cpc2007154} and derive
-+
+other interactions which are not parametrized in their work. (can add
-+
+hautman and klein's paper here and more discussion; need to put
-+
+aromatic-metal interaction approximation here)
-+
-+
+[TABULATED FORCE FIELD PARAMETERS NEEDED]
-+
-+
+\section{Computational Details}
-+
+\subsection{System Geometry}
-+
+Our simulation systems consists of a lattice Au slab with the (111)
-+
+surface perpendicular to the $z$-axis, and a solvent layer between the
-+
+periodic Au slabs along the $z$-axis. To set up the interfacial
-+
+system, the Au slab is first equilibrated without solvent under room
-+
+pressure and a desired temperature. After the metal slab is
-+
+equilibrated, United-Atom or All-Atom butanethiols are replicated on
-+
+the Au surface, each occupying the (??) among three Au atoms, and is
-+
+equilibrated under NVT ensemble. According to (CITATION), the maximal
-+
+thiol capacity on Au surface is $1/3$ of the total number of surface
-+
+Au atoms.
-+
-+
+\cite{packmol}
-+
-+
+\subsection{Simulation Parameters}
-+
-+
+When the interfacial conductance is {\it not} small, there are two
-+
+ways to define $G$. If we assume the temperature is discretely
-+
+different on two sides of the interface, $G$ can be calculated with
-+
+the thermal flux applied $J$ and the temperature difference measured
-+
+$\Delta T$ as:
-+
+\begin{equation}
-+
+G=\frac{J}{\Delta T}
-+
+\label{discreteG}
-+
+\end{equation}
-+
+We can as well assume a continuous temperature profile along the
-+
+thermal gradient axis $z$ and define $G$ as the change of bulk thermal
-+
+conductivity $\lambda$ at a defined interfacial point:
-+
+\begin{equation}
-+
+G^\prime = \Big|\frac{\partial\lambda}{\partial z}\Big|
-+
+         = \Big|\frac{\partial}{\partial z}\left(-J_z\Big/
-+
+           \left(\frac{\partial T}{\partial z}\right)\right)\Big|
-+
+         = J_z\Big|\frac{\partial^2 T}{\partial z^2}\Big|
-+
+         \Big/\left(\frac{\partial T}{\partial z}\right)^2
-+
+\label{derivativeG}
-+
+\end{equation}
-+
+With the temperature profile obtained from simulations, one is able to
-+
+approximate the first and second derivatives of $T$ with finite
-+
+difference method and thus calculate $G^\prime$.
-+
-+
+In what follows, both definitions are used for calculation and comparison.
-+
-+
+\section{Results}
-+
+\subsection{Toluene Solvent}
-+
-+
+The simulations follow a protocol similar to the previous gold/water
-+
+interfacial systems. The results (Table \ref{AuThiolToluene}) show a
-+
+significant conductance enhancement compared to the gold/water
-+
+interface without capping agent and agree with available experimental
-+
+data. This indicates that the metal-metal potential, though not
-+
+predicting an accurate bulk metal thermal conductivity, does not
-+
+greatly interfere with the simulation of the thermal conductance
-+
+behavior across a non-metal interface. The solvent model is not
-+
+particularly volatile, so the simulation cell does not expand
-+
+significantly under higher temperature. We did not observe a
-+
+significant conductance decrease when the temperature was increased to
-+
+K. The results show that the two definitions used for $G$ yield
-+
+comparable values, though $G^\prime$ tends to be smaller.
-+
-+
+\begin{table*}
-+
+  \begin{minipage}{\linewidth}
-+
+    \begin{center}
-+
+      \caption{Computed interfacial thermal conductivity ($G$ and
-+
+        $G^\prime$) values for the Au/butanethiol/toluene interface at
-+
+        different temperatures using a range of energy fluxes.}
-+
-+
+      \begin{tabular}{cccc}
-+
+        \hline\hline
-+
+        $\langle T\rangle$ & $J_z$ & $G$ & $G^\prime$ \\
-+
+        (K) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
-+
+        \hline
-+
+& 1.86 & 180 & 135 \\
-+
+            & 2.15 & 204 & 113 \\
-+
+            & 3.93 & 175 & 114 \\
-+
+& 1.91 & 143 & 125 \\
-+
+            & 4.19 & 134 & 113 \\
-+
+        \hline\hline
-+
+      \end{tabular}
-+
+      \label{AuThiolToluene}
-+
+    \end{center}
-+
+  \end{minipage}
-+
+\end{table*}
-+
-+
+\subsection{Hexane Solvent}
-+
-+
+Using the united-atom model, different coverages of capping agent,
-+
+temperatures of simulations and numbers of solvent molecules were all
-+
+investigated and Table \ref{AuThiolHexaneUA} shows the results of
-+
+these computations. The number of hexane molecules in our simulations
-+
+does not affect the calculations significantly. However, a very long
-+
+length scale for the thermal gradient axis ($z$) may cause excessively
-+
+hot or cold temperatures in the middle of the solvent region and lead
-+
+to undesired phenomena such as solvent boiling or freezing, while too
-+
+few solvent molecules would change the normal behavior of the liquid
-+
+phase. Our $N_{hexane}$ values were chosen to ensure that these
-+
+extreme cases did not happen to our simulations.
-+
-+
+Table \ref{AuThiolHexaneUA} enables direct comparison between
-+
+different coverages of capping agent, when other system parameters are
-+
+held constant. With high coverage of butanethiol on the gold surface,
-+
+the interfacial thermal conductance is enhanced
-+
+significantly. Interestingly, a slightly lower butanethiol coverage
-+
+leads to a moderately higher conductivity. This is probably due to
-+
+more solvent/capping agent contact when butanethiol molecules are
-+
+not densely packed, which enhances the interactions between the two
-+
+phases and lowers the thermal transfer barrier of this interface.
-+
+% [COMPARE TO AU/WATER IN PAPER]
-+
-+
+It is also noted that the overall simulation temperature is another
-+
+factor that affects the interfacial thermal conductance. One
-+
+possibility of this effect may be rooted in the decrease in density of
-+
+the liquid phase. We observed that when the average temperature
-+
+increases from 200K to 250K, the bulk hexane density becomes lower
-+
+than experimental value, as the system is equilibrated under NPT
-+
+ensemble. This leads to lower contact between solvent and capping
-+
+agent, and thus lower conductivity.
-+
-+
+Conductivity values are more difficult to obtain under higher
-+
+temperatures. This is because the Au surface tends to undergo
-+
+reconstructions in relatively high temperatures. Surface Au atoms can
-+
+migrate outward to reach higher Au-S contact; and capping agent
-+
+molecules can be embedded into the surface Au layer due to the same
-+
+driving force. This phenomenon agrees with experimental
-+
+results\cite{doi:10.1021/j100035a033,doi:10.1021/la026493y}. A surface
-+
+fully covered in capping agent is more susceptible to reconstruction,
-+
+possibly because fully coverage prevents other means of capping agent
-+
+relaxation, such as migration to an empty neighbor three-fold site.
-+
-+
+%MAY ADD MORE DATA TO TABLE
-+
+\begin{table*}
-+
+  \begin{minipage}{\linewidth}
-+
+    \begin{center}
-+
+      \caption{Computed interfacial thermal conductivity ($G$ and
-+
+        $G^\prime$) values for the Au/butanethiol/hexane interface
-+
+        with united-atom model and different capping agent coverage
-+
+        and solvent molecule numbers at different temperatures using a
-+
+        range of energy fluxes.}
-+
-+
+      \begin{tabular}{cccccc}
-+
+        \hline\hline
-+
+        Thiol & $\langle T\rangle$ & & $J_z$ & $G$ & $G^\prime$ \\
-+
+        coverage (\%) & (K) & $N_{hexane}$ & (GW/m$^2$) &
-+
+        \multicolumn{2}{c}{(MW/m$^2$/K)} \\
-+
+        \hline
-+
+.0   & 200 & 200 & 0.96 & 43.3 & 42.7 \\
-+
+              &     &     & 1.91 & 45.7 & 42.9 \\
-+
+              &     & 166 & 0.96 & 43.1 & 53.4 \\
-+
+.9  & 200 & 166 & 1.94 & 172  & 108  \\
-+
+.0 & 250 & 200 & 0.96 & 81.8 & 67.0 \\
-+
+              &     & 166 & 0.98 & 79.0 & 62.9 \\
-+
+              &     &     & 1.44 & 76.2 & 64.8 \\
-+
+              & 200 & 200 & 1.92 & 129  & 87.3 \\
-+
+              &     &     & 1.93 & 131  & 77.5 \\
-+
+              &     & 166 & 0.97 & 115  & 69.3 \\
-+
+              &     &     & 1.94 & 125  & 87.1 \\
-+
+        \hline\hline
-+
+      \end{tabular}
-+
+      \label{AuThiolHexaneUA}
-+
+    \end{center}
-+
+  \end{minipage}
-+
+\end{table*}
-+
-+
+For the all-atom model, the liquid hexane phase was not stable under NPT
-+
+conditions. Therefore, the simulation length scale parameters are
-+
+adopted from previous equilibration results of the united-atom model
-+
+at 200K. Table \ref{AuThiolHexaneAA} shows the results of these
-+
+simulations. The conductivity values calculated with full capping
-+
+agent coverage are substantially larger than observed in the
-+
+united-atom model, and is even higher than predicted by
-+
+experiments. It is possible that our parameters for metal-non-metal
-+
+particle interactions lead to an overestimate of the interfacial
-+
+thermal conductivity, although the active C-H vibrations in the
-+
+all-atom model (which should not be appreciably populated at normal
-+
+temperatures) could also account for this high conductivity. The major
-+
+thermal transfer barrier of Au/butanethiol/hexane interface is between
-+
+the liquid phase and the capping agent, so extra degrees of freedom
-+
+such as the C-H vibrations could enhance heat exchange between these
-+
+two phases and result in a much higher conductivity.
-+
-+
+\begin{table*}
-+
+  \begin{minipage}{\linewidth}
-+
+    \begin{center}
-+
-+
+      \caption{Computed interfacial thermal conductivity ($G$ and
-+
+        $G^\prime$) values for the Au/butanethiol/hexane interface
-+
+        with all-atom model and different capping agent coverage at
-+
+K using a range of energy fluxes.}
-+
-+
+      \begin{tabular}{cccc}
-+
+        \hline\hline
-+
+        Thiol & $J_z$ & $G$ & $G^\prime$ \\
-+
+        coverage (\%) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
-+
+        \hline
-+
+.0   & 0.95 & 28.5 & 27.2 \\
-+
+              & 1.88 & 30.3 & 28.9 \\
-+
+.0 & 2.87 & 551  & 294  \\
-+
+              & 3.81 & 494  & 193  \\
-+
+        \hline\hline
-+
+      \end{tabular}
-+
+      \label{AuThiolHexaneAA}
-+
+    \end{center}
-+
+  \end{minipage}
-+
+\end{table*}
-+
-+
+%subsubsection{Vibrational spectrum study on conductance mechanism}
-+
+To investigate the mechanism of this interfacial thermal conductance,
-+
+the vibrational spectra of various gold systems were obtained and are
-+
+shown as in the upper panel of Fig. \ref{vibration}. To obtain these
-+
+spectra, one first runs a simulation in the NVE ensemble and collects
-+
+snapshots of configurations; these configurations are used to compute
-+
+the velocity auto-correlation functions, which is used to construct a
-+
+power spectrum via a Fourier transform. The gold surfaces covered by
-+
+butanethiol molecules exhibit an additional peak observed at a
-+
+frequency of $\sim$170cm$^{-1}$, which is attributed to the vibration
-+
+of the S-Au bond. This vibration enables efficient thermal transport
-+
+from surface Au atoms to the capping agents. Simultaneously, as shown
-+
+in the lower panel of Fig. \ref{vibration}, the large overlap of the
-+
+vibration spectra of butanethiol and hexane in the all-atom model,
-+
+including the C-H vibration, also suggests high thermal exchange
-+
+efficiency. The combination of these two effects produces the drastic
-+
+interfacial thermal conductance enhancement in the all-atom model.
-+
-+
+\begin{figure}
-+
+\includegraphics[width=\linewidth]{vibration}
-+
+\caption{Vibrational spectra obtained for gold in different
-+
+  environments (upper panel) and for Au/thiol/hexane simulation in
-+
+  all-atom model (lower panel).}
-+
+\label{vibration}
-+
+\end{figure}
-+
+% 600dpi, letter size. too large?
-+
-+
+\section{Acknowledgments}
+Support for this project was provided by the National Science
+Foundation under grant CHE-0848243. Computational time was provided by

Diff Legend

-–
+Removed lines
-+
+Added lines
-<
+Changed lines
->
+Changed lines

Comparing interfacial/interfacial.tex (file contents): Revision 3717 by gezelter, Thu Jan 27 16:29:20 2011 UTC vs. Revision 3725 by skuang, Mon May 9 19:08:08 2011 UTC

Diff Legend

Comparing interfacial/interfacial.tex (file contents):
Revision 3717 by gezelter, Thu Jan 27 16:29:20 2011 UTC vs.
Revision 3725 by skuang, Mon May 9 19:08:08 2011 UTC