--- interfacial/interfacial.tex	2011/07/05 21:30:29	3731
+++ interfacial/interfacial.tex	2011/07/08 17:07:00	3732
@@ -45,20 +45,22 @@ We have developed a Non-Isotropic Velocity Scaling alg
 
 \begin{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.
+With the Non-Isotropic Velocity Scaling algorithm (NIVS) we have
+developed, an unphysical thermal flux can be effectively set up even
+for non-homogeneous systems like interfaces in non-equilibrium
+molecular dynamics simulations. In this work, this algorithm is
+applied for simulating thermal conductance at metal / organic solvent
+interfaces with various coverages of butanethiol capping
+agents. Different solvents and force field models were tested. Our
+results suggest that the United-Atom models are able to provide an
+estimate of the interfacial thermal conductivity comparable to
+experiments in our simulations with satisfactory computational
+efficiency. From our results, the acoustic impedance mismatch between
+metal and liquid phase is effectively reduced by the capping
+agents, and thus leads to interfacial thermal conductance
+enhancement. Furthermore, this effect is closely related to the
+capping agent coverage on the metal surfaces and the type of solvent
+molecules, and is affected by the models used in the simulations.
 
 \end{abstract}
 
@@ -370,7 +372,8 @@ parameters in our simulations.
       
       \begin{tabular}{ccc}
         \hline\hline
-        Non-metal & $\sigma$/\AA & $\epsilon$/kcal/mol \\
+        Non-metal atom   & $\sigma$ & $\epsilon$ \\
+        (or pseudo-atom) & \AA      & kcal/mol  \\
         \hline
         S    & 2.40   & 8.465   \\
         CH3  & 3.54   & 0.2146  \\
@@ -456,7 +459,7 @@ couple $J_z$'s and do not need to test a large series 
         \hline\hline
         $\langle T\rangle$ & & $L_x$ & $L_y$ & $L_z$ & $J_z$ &
         $G$ & $G^\prime$ \\
-        (K) & $N_{hexane}$ & \multicolumn{3}{c}\AA & (GW/m$^2$) &
+        (K) & $N_{hexane}$ & \multicolumn{3}{c}{(\AA)} & (GW/m$^2$) &
         \multicolumn{2}{c}{(MW/m$^2$/K)} \\
         \hline
         200 & 266 & 29.86 & 25.80 & 113.1 & -0.96 &
@@ -551,7 +554,7 @@ undertaken at $<T>\sim$200K.
 reconstructions could eliminate the original $x$ and $y$ dimensional
 homogeneity, measurement of $G$ is more difficult to conduct under
 higher temperatures. Therefore, most of our measurements are
-undertaken at $<T>\sim$200K.
+undertaken at $\langle T\rangle\sim$200K.
 
 However, when the surface is not completely covered by butanethiols,
 the simulated system is more resistent to the reconstruction
@@ -616,7 +619,7 @@ differences in the IR range do not seem to produce an 
 butanethiol (UA) is non-deuterated for both solvents. These UA model
 studies, even though eliminating C-H vibration samplings, still have
 C-C vibrational frequencies different from each other. However, these
-differences in the IR range do not seem to produce an observable
+differences in the infrared range do not seem to produce an observable
 difference for the results of $G$. [MAY NEED FIGURE]
 
 Furthermore, results for rigid body toluene solvent, as well as other
@@ -642,22 +645,22 @@ can see a plateau of $G$ vs. butanethiol coverage in o
 \begin{table*}
   \begin{minipage}{\linewidth}
     \begin{center}
-      \caption{Computed interfacial thermal conductivity ($G$ in
-        MW/m$^2$/K) values for the Au-butanethiol/solvent interface
-        with various UA models and different capping agent coverages
-        at $<T>\sim$200K using certain energy flux respectively.}
+      \caption{Computed interfacial thermal conductivity ($G$) values
+        for the Au-butanethiol/solvent interface with various UA
+        models and different capping agent coverages at $\langle
+        T\rangle\sim$200K using certain energy flux respectively.}
       
       \begin{tabular}{cccc}
         \hline\hline
-        Thiol & & & \\
-        coverage (\%) & hexane & hexane-D & toluene \\
+        Thiol & \multicolumn{3}{c}{$G$(MW/m$^2$/K)} \\
+        coverage (\%) & hexane & hexane(D) & toluene \\
         \hline
-        0.0   & 46.5 & 43.9 & 70.1 \\
-        25.0  & 151  & 153  & 249  \\
-        50.0  & 172  & 182  & 214  \\
-        75.0  & 242  & 229  & 244  \\
-        88.9  & 178  & -    & -    \\
-        100.0 & 137  & 153  & 187  \\
+        0.0   & 46.5() & 43.9() & 70.1() \\
+        25.0  & 151()  & 153()  & 249()  \\
+        50.0  & 172()  & 182()  & 214()  \\
+        75.0  & 242()  & 229()  & 244()  \\
+        88.9  & 178()  & -      & -      \\
+        100.0 & 137()  & 153()  & 187()  \\
         \hline\hline
       \end{tabular}
       \label{tlnUhxnUhxnD}
@@ -668,82 +671,115 @@ For the all-atom model, the liquid hexane phase was no
 \subsection{Influence of Chosen Molecule Model on $G$}
 [MAY COMBINE W MECHANISM STUDY]
 
-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.
+In addition to UA solvent/capping agent models, AA models are included
+in our simulations as well. Besides simulations of the same (UA or AA)
+model for solvent and capping agent, different models can be applied
+to different components. Furthermore, regardless of models chosen,
+either the solvent or the capping agent can be deuterated, similar to
+the previous section. Table \ref{modelTest} summarizes the results of
+these studies.
 
+[MORE DATA; ERROR ESTIMATE]
 \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
-        200K using a range of energy fluxes.}
+        $G^\prime$) values for interfaces using various models for
+        solvent and capping agent (or without capping agent) at
+        $\langle T\rangle\sim$200K.}
       
-      \begin{tabular}{cccc}
+      \begin{tabular}{ccccc}
         \hline\hline
-        Thiol & $J_z$ & $G$ & $G^\prime$ \\
-        coverage (\%) & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\
+        Butanethiol model & Solvent & $J_z$ & $G$ & $G^\prime$ \\
+        (or bare surface) & model & (GW/m$^2$) &
+        \multicolumn{2}{c}{(MW/m$^2$/K)} \\
         \hline
-        0.0   & 0.95 & 28.5 & 27.2 \\
-              & 1.88 & 30.3 & 28.9 \\
-        100.0 & 2.87 & 551  & 294  \\
-              & 3.81 & 494  & 193  \\
+        UA    & AA hexane  & 1.94 & 135()  & 129()  \\
+              &            & 2.86 & 126()  & 115()  \\
+              & AA toluene & 1.89 & 200()  & 149()  \\
+        AA    & UA hexane  & 1.94 & 116()  & 129()  \\
+              & AA hexane  & 3.76 & 451()  & 378()  \\
+              &            & 4.71 & 432()  & 334()  \\
+              & AA toluene & 3.79 & 487()  & 290()  \\
+        AA(D) & UA hexane  & 1.94 & 158()  & 172()  \\
+        bare  & AA hexane  & 0.96 & 31.0() & 29.4() \\
         \hline\hline
       \end{tabular}
-      \label{AuThiolHexaneAA}
+      \label{modelTest}
     \end{center}
   \end{minipage}
 \end{table*}
 
+To facilitate direct comparison, the same system with differnt models
+for different components uses the same length scale for their
+simulation cells. Without the presence of capping agent, using
+different models for hexane yields similar results for both $G$ and
+$G^\prime$, and these two definitions agree with eath other very
+well. This indicates very weak interaction between the metal and the
+solvent, and is a typical case for acoustic impedance mismatch between
+these two phases.
 
-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. 
+As for Au(111) surfaces completely covered by butanethiols, the choice
+of models for capping agent and solvent could impact the measurement
+of $G$ and $G^\prime$ quite significantly. For Au-butanethiol/hexane
+interfaces, using AA model for both butanethiol and hexane yields
+substantially higher conductivity values than using UA model for at
+least one component of the solvent and capping agent, which exceeds
+the upper bond of experimental value range. This is probably due to
+the classically treated C-H vibrations in the AA model, which should
+not be appreciably populated at normal temperatures. In comparison,
+once either the hexanes or the butanethiols are deuterated, one can
+see a significantly lower $G$ and $G^\prime$. In either of these
+cases, the C-H(D) vibrational overlap between the solvent and the
+capping agent is removed. [MAY NEED FIGURE] Conclusively, the
+improperly treated C-H vibration in the AA model produced
+over-predicted results accordingly. Compared to the AA model, the UA
+model yields more reasonable results with higher computational
+efficiency.
 
-% The results show that the two definitions used for $G$ yield
-% comparable values, though $G^\prime$ tends to be smaller.
+However, for Au-butanethiol/toluene interfaces, having the AA
+butanethiol deuterated did not yield a significant change in the
+measurement results.
+. , 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.
 
+
+Although the QSC model for Au is known to predict an overly low value
+for bulk metal gold conductivity[CITE NIVSRNEMD], our computational
+results for $G$ and $G^\prime$ do not seem to be affected by this
+drawback of the model for metal. Instead, the modeling of interfacial
+thermal transport behavior relies mainly on an accurate description of
+the interactions between components occupying the interfaces.
+
 \subsection{Mechanism of Interfacial Thermal Conductance Enhancement
   by Capping Agent}
-[MAY INTRODUCE PROTOCOL IN METHODOLOGY/COMPUTATIONAL DETAIL]
+%OR\subsection{Vibrational spectrum study on conductance mechanism}
 
+[MAY INTRODUCE PROTOCOL IN METHODOLOGY/COMPUTATIONAL DETAIL, EQN'S]
 
-%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.
+power spectrum via a Fourier transform.
 
+ The gold surfaces covered by
+butanethiol molecules, compared to bare gold surfaces, 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.
+
+[MAY NEED TO CONVERT TO JPEG]
 \begin{figure}
 \includegraphics[width=\linewidth]{vibration}
 \caption{Vibrational spectra obtained for gold in different
@@ -751,13 +787,43 @@ interfacial thermal conductance enhancement in the all
   all-atom model (lower panel).}
 \label{vibration}
 \end{figure}
-% MAY NEED TO CONVERT TO JPEG
 
+[COMPARISON OF TWO G'S; AU SLAB WIDTHS; ETC]
+% The results show that the two definitions used for $G$ yield
+% comparable values, though $G^\prime$ tends to be smaller.
+
 \section{Conclusions}
+The NIVS algorithm we developed has been applied to simulations of
+Au-butanethiol surfaces with organic solvents. This algorithm allows
+effective unphysical thermal flux transferred between the metal and
+the liquid phase. With the flux applied, we were able to measure the
+corresponding thermal gradient and to obtain interfacial thermal
+conductivities. Our simulations have seen significant conductance
+enhancement with the presence of capping agent, compared to the bare
+gold/liquid interfaces. The acoustic impedance mismatch between the
+metal and the liquid phase is effectively eliminated by proper capping
+agent. Furthermore, the coverage precentage of the capping agent plays
+an important role in the interfacial thermal transport process.
 
+Our measurement results, particularly of the UA models, agree with
+available experimental data. This indicates that our force field
+parameters have a nice description of the interactions between the
+particles at the interfaces. AA models tend to overestimate the
+interfacial thermal conductance in that the classically treated C-H
+vibration would be overly sampled. Compared to the AA models, the UA
+models have higher computational efficiency with satisfactory
+accuracy, and thus are preferable in interfacial thermal transport
+modelings.
 
-[NECESSITY TO STUDY THERMAL CONDUCTANCE IN NANOCRYSTAL STRUCTURE]\cite{vlugt:cpc2007154}
+Vlugt {\it et al.} has investigated the surface thiol structures for
+nanocrystal gold and pointed out that they differs from those of the
+Au(111) surface\cite{vlugt:cpc2007154}. This difference might lead to
+change of interfacial thermal transport behavior as well. To
+investigate this problem, an effective means to introduce thermal flux
+and measure the corresponding thermal gradient is desirable for
+simulating structures with spherical symmetry.
 
+
 \section{Acknowledgments}
 Support for this project was provided by the National Science
 Foundation under grant CHE-0848243. Computational time was provided by
