--- interfacial/interfacial.tex 2011/07/14 19:49:12 3739 +++ interfacial/interfacial.tex 2011/07/15 17:55:16 3742 @@ -23,8 +23,8 @@ \setlength{\belowcaptionskip}{30 pt} %\renewcommand\citemid{\ } % no comma in optional reference note -\bibpunct{[}{]}{,}{s}{}{;} -\bibliographystyle{aip} +\bibpunct{[}{]}{,}{n}{}{;} +\bibliographystyle{achemso} \begin{document} @@ -227,9 +227,16 @@ illustrated in Figure \ref{demoPic}. illustrated in Figure \ref{demoPic}. \begin{figure} -\includegraphics[width=\linewidth]{demoPic} -\caption{A sample showing how a metal slab has its (111) surface - covered by capping agent molecules and solvated by hexane.} +\includegraphics[width=\linewidth]{method} +\caption{Interfacial conductance can be calculated by applying an + (unphysical) kinetic energy flux between two slabs, one located + within the metal and another on the edge of the periodic box. The + system responds by forming a thermal response or a gradient. In + bulk liquids, this gradient typically has a single slope, but in + interfacial systems, there are distinct thermal conductivity + domains. The interfacial conductance, $G$ is found by measuring the + temperature gap at the Gibbs dividing surface, or by using second + derivatives of the thermal profile.} \label{demoPic} \end{figure} @@ -332,9 +339,14 @@ organic solvent molecules in our simulations. organic solvent molecules in our simulations. \begin{figure} -\includegraphics[width=\linewidth]{demoMol} -\caption{Denomination of atoms or pseudo-atoms in our simulations: a) - UA-hexane; b) AA-hexane; c) UA-toluene; d) AA-toluene.} +\includegraphics[width=\linewidth]{structures} +\caption{Structures of the capping agent and solvents utilized in + these simulations. The chemically-distinct sites (a-e) are expanded + in terms of constituent atoms for both United Atom (UA) and All Atom + (AA) force fields. Most parameters are from + Refs. \protect\cite{TraPPE-UA.alkanes,TraPPE-UA.alkylbenzenes} (UA) and + \protect\cite{OPLSAA} (AA). Cross-interactions with the Au atoms are given + in Table \ref{MnM}.} \label{demoMol} \end{figure} @@ -377,8 +389,8 @@ Lorentz-Berthelot Mixing Rule: interactions between capping agent and solvent can be derived using Lorentz-Berthelot Mixing Rule: \begin{eqnarray} -\sigma_{IJ} & = & \frac{1}{2} \left(\sigma_{II} + \sigma_{JJ}\right) \\ -\epsilon_{IJ} & = & \sqrt{\epsilon_{II}\epsilon_{JJ}} +\sigma_{ij} & = & \frac{1}{2} \left(\sigma_{ii} + \sigma_{jj}\right) \\ +\epsilon_{ij} & = & \sqrt{\epsilon_{ii}\epsilon_{jj}} \end{eqnarray} To describe the interactions between metal Au and non-metal capping @@ -408,27 +420,30 @@ parameters in our simulations. \begin{table*} \begin{minipage}{\linewidth} \begin{center} - \caption{Non-bonded interaction paramters for non-metal - particles and metal-non-metal interactions in our - simulations.} - - \begin{tabular}{cccccc} + \caption{Non-bonded interaction parameters (including cross + interactions with Au atoms) for both force fields used in this + work.} + \begin{tabular}{lllllll} \hline\hline - Non-metal atom $I$ & $\sigma_{II}$ & $\epsilon_{II}$ & $q_I$ & - $\sigma_{AuI}$ & $\epsilon_{AuI}$ \\ - (or pseudo-atom) & \AA & kcal/mol & & \AA & kcal/mol \\ + & Site & $\sigma_{ii}$ & $\epsilon_{ii}$ & $q_i$ & + $\sigma_{Au-i}$ & $\epsilon_{Au-i}$ \\ + & & (\AA) & (kcal/mol) & ($e$) & (\AA) & (kcal/mol) \\ \hline - CH3 & 3.75 & 0.1947 & - & 3.54 & 0.2146 \\ - CH2 & 3.95 & 0.0914 & - & 3.54 & 0.1749 \\ - CHar & 3.695 & 0.1003 & - & 3.4625 & 0.1680 \\ - CRar & 3.88 & 0.04173 & - & 3.555 & 0.1604 \\ - S & 4.45 & 0.25 & - & 2.40 & 8.465 \\ - CT3 & 3.50 & 0.066 & -0.18 & 3.365 & 0.1373 \\ - CT2 & 3.50 & 0.066 & -0.12 & 3.365 & 0.1373 \\ - CTT & 3.50 & 0.066 & -0.065 & 3.365 & 0.1373 \\ - HC & 2.50 & 0.030 & 0.06 & 2.865 & 0.09256 \\ - CA & 3.55 & 0.070 & -0.115 & 3.173 & 0.0640 \\ - HA & 2.42 & 0.030 & 0.115 & 2.746 & 0.0414 \\ + United Atom (UA) + &CH3 & 3.75 & 0.1947 & - & 3.54 & 0.2146 \\ + &CH2 & 3.95 & 0.0914 & - & 3.54 & 0.1749 \\ + &CHar & 3.695 & 0.1003 & - & 3.4625 & 0.1680 \\ + &CRar & 3.88 & 0.04173 & - & 3.555 & 0.1604 \\ + \hline + All Atom (AA) + &CT3 & 3.50 & 0.066 & -0.18 & 3.365 & 0.1373 \\ + &CT2 & 3.50 & 0.066 & -0.12 & 3.365 & 0.1373 \\ + &CTT & 3.50 & 0.066 & -0.065 & 3.365 & 0.1373 \\ + &HC & 2.50 & 0.030 & 0.06 & 2.865 & 0.09256 \\ + &CA & 3.55 & 0.070 & -0.115 & 3.173 & 0.0640 \\ + &HA & 2.42 & 0.030 & 0.115 & 2.746 & 0.0414 \\ + \hline + Both UA and AA & S & 4.45 & 0.25 & - & 2.40 & 8.465 \\ \hline\hline \end{tabular} \label{MnM} @@ -688,7 +703,6 @@ can see a plateau of $G$ vs. butanethiol coverage in o 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] \begin{figure} \includegraphics[width=\linewidth]{coverage} \caption{Comparison of interfacial thermal conductivity ($G$) values @@ -709,7 +723,6 @@ these studies. the previous section. Table \ref{modelTest} summarizes the results of these studies. -[MORE DATA; ERROR ESTIMATE] \begin{table*} \begin{minipage}{\linewidth} \begin{center} @@ -719,35 +732,35 @@ these studies. solvent and capping agent (or without capping agent) at $\langle T\rangle\sim$200K. (D stands for deuterated solvent or capping agent molecules; ``Avg.'' denotes results that are - averages of several simulations.)} + averages of simulations under different $J_z$'s. Error + estimates indicated in parenthesis.)} - \begin{tabular}{ccccc} + \begin{tabular}{llccc} \hline\hline Butanethiol model & Solvent & $J_z$ & $G$ & $G^\prime$ \\ (or bare surface) & model & (GW/m$^2$) & \multicolumn{2}{c}{(MW/m$^2$/K)} \\ \hline - UA & UA hexane & Avg. & 131() & 86.5() \\ - & UA hexane(D) & 1.95 & 153() & 136() \\ - & AA hexane & 1.94 & 135() & 129() \\ - & & 2.86 & 126() & 115() \\ - & UA toluene & 1.96 & 187() & 151() \\ - & AA toluene & 1.89 & 200() & 149() \\ + UA & UA hexane & Avg. & 131(9) & 87(10) \\ + & UA hexane(D) & 1.95 & 153(5) & 136(13) \\ + & AA hexane & Avg. & 131(6) & 122(10) \\ + & UA toluene & 1.96 & 187(16) & 151(11) \\ + & AA toluene & 1.89 & 200(36) & 149(53) \\ \hline - AA & UA hexane & 1.94 & 116() & 129() \\ - & AA hexane & Avg. & 442() & 356() \\ - & AA hexane(D) & 1.93 & 222() & 234() \\ - & UA toluene & 1.98 & 125() & 96.5() \\ - & AA toluene & 3.79 & 487() & 290() \\ + AA & UA hexane & 1.94 & 116(9) & 129(8) \\ + & AA hexane & Avg. & 442(14) & 356(31) \\ + & AA hexane(D) & 1.93 & 222(12) & 234(54) \\ + & UA toluene & 1.98 & 125(25) & 97(60) \\ + & AA toluene & 3.79 & 487(56) & 290(42) \\ \hline - AA(D) & UA hexane & 1.94 & 158() & 172() \\ - & AA hexane & 1.92 & 243() & 191() \\ - & AA toluene & 1.93 & 364() & 322() \\ + AA(D) & UA hexane & 1.94 & 158(25) & 172(4) \\ + & AA hexane & 1.92 & 243(29) & 191(11) \\ + & AA toluene & 1.93 & 364(36) & 322(67) \\ \hline - bare & UA hexane & Avg. & 46.5() & 49.4() \\ - & UA hexane(D) & 0.98 & 43.9() & 43.0() \\ - & AA hexane & 0.96 & 31.0() & 29.4() \\ - & UA toluene & 1.99 & 70.1() & 65.8() \\ + bare & UA hexane & Avg. & 46.5(3.2) & 49.4(4.5) \\ + & UA hexane(D) & 0.98 & 43.9(4.6) & 43.0(2.0) \\ + & AA hexane & 0.96 & 31.0(1.4) & 29.4(1.3) \\ + & UA toluene & 1.99 & 70.1(1.3) & 65.8(0.5) \\ \hline\hline \end{tabular} \label{modelTest}