--- interfacial/interfacial.tex 2011/07/05 17:39:21 3730 +++ interfacial/interfacial.tex 2011/07/05 21:30:29 3731 @@ -448,28 +448,33 @@ couple $J_z$'s and do not need to test a large series \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} + $G^\prime$) values for the 100\% covered Au-butanethiol/hexane + interfaces with UA model and different hexane molecule numbers + at different temperatures using a range of energy fluxes.} + + \begin{tabular}{cccccccc} \hline\hline - Thiol & $\langle T\rangle$ & & $J_z$ & $G$ & $G^\prime$ \\ - coverage (\%) & (K) & $N_{hexane}$ & (GW/m$^2$) & + $\langle T\rangle$ & & $L_x$ & $L_y$ & $L_z$ & $J_z$ & + $G$ & $G^\prime$ \\ + (K) & $N_{hexane}$ & \multicolumn{3}{c}\AA & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\ \hline - 0.0 & 200 & 200 & 0.96 & 43.3 & 42.7 \\ - & & & 1.91 & 45.7 & 42.9 \\ - & & 166 & 0.96 & 43.1 & 53.4 \\ - 88.9 & 200 & 166 & 1.94 & 172 & 108 \\ - 100.0 & 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 \\ + 200 & 266 & 29.86 & 25.80 & 113.1 & -0.96 & + 102() & 80.0() \\ + & 200 & 29.84 & 25.81 & 93.9 & 1.92 & + 129() & 87.3() \\ + & & 29.84 & 25.81 & 95.3 & 1.93 & + 131() & 77.5() \\ + & 166 & 29.84 & 25.81 & 85.7 & 0.97 & + 115() & 69.3() \\ + & & & & & 1.94 & + 125() & 87.1() \\ + 250 & 200 & 29.84 & 25.87 & 106.8 & 0.96 & + 81.8() & 67.0() \\ + & 166 & 29.87 & 25.84 & 94.8 & 0.98 & + 79.0() & 62.9() \\ + & & 29.84 & 25.85 & 95.0 & 1.44 & + 76.2() & 64.8() \\ \hline\hline \end{tabular} \label{AuThiolHexaneUA} @@ -500,24 +505,25 @@ in that higher degree of contact could yield increased important role in the thermal transport process across the interface in that higher degree of contact could yield increased conductance. -[ADD SIGNS AND ERROR ESTIMATE TO TABLE] +[ADD Lxyz AND ERROR ESTIMATE TO TABLE] \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.} + $G^\prime$) values for a 90\% coverage 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 - 200 & 1.86 & 180 & 135 \\ - & 2.15 & 204 & 113 \\ - & 3.93 & 175 & 114 \\ - 300 & 1.91 & 143 & 125 \\ - & 4.19 & 134 & 113 \\ + 200 & -1.86 & 180() & 135() \\ + & 2.15 & 204() & 113() \\ + & -3.93 & 175() & 114() \\ + 300 & -1.91 & 143() & 125() \\ + & -4.19 & 134() & 113() \\ \hline\hline \end{tabular} \label{AuThiolToluene} @@ -565,54 +571,93 @@ different coverages of butanethiol. molecules. These systems are then equilibrated and their interfacial thermal conductivity are measured with our NIVS algorithm. Table \ref{tlnUhxnUhxnD} lists these results for direct comparison between -different coverages of butanethiol. +different coverages of butanethiol. To study the isotope effect in +interfacial thermal conductance, deuterated UA-hexane is included as +well. - 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 turned out that with partial covered butanethiol on the Au(111) +surface, the derivative definition for $G$ (Eq. \ref{derivativeG}) has +difficulty to apply, due to the difficulty in locating the maximum of +change of $\lambda$. Instead, the discrete definition +(Eq. \ref{discreteG}) is easier to apply, as max($\Delta T$) can still +be well-defined. Therefore, $G$'s (not $G^\prime$) are used for this +section. +From Table \ref{tlnUhxnUhxnD}, one can see the significance of the +presence of capping agents. Even when a fraction of the Au(111) +surface sites are covered with butanethiols, the conductivity would +see an enhancement by at least a factor of 3. This indicates the +important role cappping agent is playing for thermal transport +phenomena on metal/organic solvent surfaces. -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 results show that the two definitions used for $G$ yield -comparable values, though $G^\prime$ tends to be smaller. +Interestingly, as one could observe from our results, the maximum +conductance enhancement (largest $G$) happens while the surfaces are +about 75\% covered with butanethiols. This again indicates that +solvent-capping agent contact has an important role of the thermal +transport process. Slightly lower butanethiol coverage allows small +gaps between butanethiols to form. And these gaps could be filled with +solvent molecules, which acts like ``heat conductors'' on the +surface. The higher degree of interaction between these solvent +molecules and capping agents increases the enhancement effect and thus +produces a higher $G$ than densely packed butanethiol arrays. However, +once this maximum conductance enhancement is reached, $G$ decreases +when butanethiol coverage continues to decrease. Each capping agent +molecule reaches its maximum capacity for thermal +conductance. Therefore, even higher solvent-capping agent contact +would not offset this effect. Eventually, when butanethiol coverage +continues to decrease, solvent-capping agent contact actually +decreases with the disappearing of butanethiol molecules. In this +case, $G$ decrease could not be offset but instead accelerated. +A comparison of the results obtained from differenet organic solvents +can also provide useful information of the interfacial thermal +transport process. The deuterated hexane (UA) results do not appear to +be much different from those of normal hexane (UA), given that +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 +difference for the results of $G$. [MAY NEED FIGURE] +Furthermore, results for rigid body toluene solvent, as well as other +UA-hexane solvents, are reasonable within the general experimental +ranges[CITATIONS]. This suggests that explicit hydrogen might not be a +required factor for modeling thermal transport phenomena of systems +such as Au-thiol/organic solvent. + +However, results for Au-butanethiol/toluene do not show an identical +trend with those for Au-butanethiol/hexane in that $G$'s remain at +approximately the same magnitue when butanethiol coverage differs from +25\% to 75\%. This might be rooted in the molecule shape difference +for plane-like toluene and chain-like {\it n}-hexane. Due to this +difference, toluene molecules have more difficulty in occupying +relatively small gaps among capping agents when their coverage is not +too low. Therefore, the solvent-capping agent contact may keep +increasing until the capping agent coverage reaches a relatively low +level. This becomes an offset for decreasing butanethiol molecules on +its effect to the process of interfacial thermal transport. Thus, one +can see a plateau of $G$ vs. butanethiol coverage in our results. + +[NEED ERROR ESTIMATE, MAY ALSO PUT J HERE] \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.} + \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.} - \begin{tabular}{cccccc} + \begin{tabular}{cccc} \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)} \\ + Thiol & & & \\ + coverage (\%) & hexane & hexane-D & toluene \\ \hline - 0.0 & 200 & 200 & 0.96 & 43.3 & 42.7 \\ - & & & 1.91 & 45.7 & 42.9 \\ - & & 166 & 0.96 & 43.1 & 53.4 \\ - 88.9 & 200 & 166 & 1.94 & 172 & 108 \\ - 100.0 & 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 \\ + 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} @@ -666,6 +711,16 @@ two phases and result in a much higher conductivity. \end{table*} +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 results show that the two definitions used for $G$ yield +% comparable values, though $G^\prime$ tends to be smaller. + \subsection{Mechanism of Interfacial Thermal Conductance Enhancement by Capping Agent} [MAY INTRODUCE PROTOCOL IN METHODOLOGY/COMPUTATIONAL DETAIL]