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