--- 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 $\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 $\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 $\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