| 1 |
skucera |
4375 |
\documentclass[aps,jcp,preprint,showpacs,superscriptaddress,groupedaddress]{revtex4} % for double-spaced preprint |
| 2 |
|
|
\usepackage{graphicx} % needed for figures |
| 3 |
|
|
\usepackage{dcolumn} % needed for some tables |
| 4 |
|
|
\usepackage{bm} % for math |
| 5 |
|
|
\usepackage{amssymb} % for math |
| 6 |
|
|
%\usepackage{booktabs} |
| 7 |
|
|
\usepackage[english]{babel} |
| 8 |
|
|
\usepackage{multirow} |
| 9 |
|
|
\usepackage{tablefootnote} |
| 10 |
|
|
\usepackage{times} |
| 11 |
|
|
\usepackage[version=3]{mhchem} |
| 12 |
|
|
\usepackage{lineno} |
| 13 |
|
|
\usepackage{gensymb} |
| 14 |
gezelter |
4376 |
\usepackage{multirow} |
| 15 |
skucera |
4375 |
|
| 16 |
|
|
\begin{document} |
| 17 |
|
|
|
| 18 |
|
|
\title{Supporting Information for: Interfacial Thermal Conductance of Thiolate-Protected |
| 19 |
|
|
Gold Nanospheres} |
| 20 |
|
|
\author{Kelsey M. Stocker} |
| 21 |
|
|
\author{Suzanne M. Neidhart} |
| 22 |
|
|
\author{J. Daniel Gezelter} |
| 23 |
|
|
\email{gezelter@nd.edu} |
| 24 |
|
|
\affiliation{Department of Chemistry and Biochemistry, University of |
| 25 |
|
|
Notre Dame, Notre Dame, IN 46556} |
| 26 |
|
|
|
| 27 |
|
|
\maketitle |
| 28 |
gezelter |
4379 |
Gold -- gold interactions were described by the quantum Sutton-Chen |
| 29 |
|
|
(QSC) model.\cite{Qi:1999ph} The hexane solvent is described by the |
| 30 |
|
|
TraPPE united atom model,\cite{TraPPE-UA.alkanes} where sites are |
| 31 |
|
|
located at the carbon centers for alkyl groups. Bonding interactions |
| 32 |
|
|
were used for intra-molecular sites closer than 3 bonds. Effective |
| 33 |
|
|
Lennard-Jones potentials were used for non-bonded interactions. |
| 34 |
|
|
|
| 35 |
gezelter |
4381 |
\begin{table}[h] |
| 36 |
|
|
\centering |
| 37 |
|
|
\caption{Properties of the United atom sites. \label{tab:atypes}} |
| 38 |
|
|
\begin{tabular}{ c|cccc } |
| 39 |
|
|
\toprule |
| 40 |
|
|
atom type & mass (amu)& $\epsilon$ (kcal/mol) & $\sigma$ (\AA) & source \\ |
| 41 |
|
|
\colrule |
| 42 |
|
|
\ce{CH3} & 15.04 & 0.1947 & 3.75 & \\ |
| 43 |
|
|
\ce{CH2} & 14.03 & 0.09141 & 3.95 & \\ |
| 44 |
|
|
\ce{CH} & 13.02 & 0.01987 & 4.68 & \\ |
| 45 |
|
|
\ce{CHene} & 13.02 & 0.09340 & 3.73 & \\ |
| 46 |
|
|
\ce{CH2ene} & 14.03 & 0.16891 & 3.675 & \\ |
| 47 |
|
|
S & 32.0655 & 0.2504 & 4.45 & Refs. \protect\cite{landman:1998} ($\sigma$) and \protect\cite{vlugt:cpc2007154} ($\epsilon$) \\ |
| 48 |
|
|
\ce{CHar} & 13.02 & 0.1004 & 3.695 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
| 49 |
|
|
\ce{CH2ar} & 14.03 & 0.1004 & 3.695 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
| 50 |
|
|
\botrule |
| 51 |
|
|
\end{tabular} |
| 52 |
|
|
\end{table} |
| 53 |
|
|
|
| 54 |
gezelter |
4379 |
The TraPPE-UA force field includes parameters for thiol |
| 55 |
|
|
molecules\cite{TraPPE-UA.thiols} which were used for the |
| 56 |
|
|
alkanethiolate molecules in our simulations. To derive suitable |
| 57 |
|
|
parameters for butanethiolate adsorbed on Au(111) surfaces, we adopted |
| 58 |
|
|
the S parameters from Luedtke and Landman\cite{landman:1998} and |
| 59 |
|
|
modified the parameters for the CTS atom to maintain charge neutrality |
| 60 |
|
|
in the molecule. |
| 61 |
|
|
|
| 62 |
gezelter |
4381 |
Bonds are typically rigid in TraPPE-UA, and for flexible bonds, we |
| 63 |
|
|
utilized bond stretching spring constants from |
| 64 |
|
|
|
| 65 |
|
|
\begin{table}[h] |
| 66 |
|
|
\centering |
| 67 |
|
|
\caption{Bond parameters. \label{tab:bond}} |
| 68 |
|
|
\begin{tabular}{ cc|lll } |
| 69 |
|
|
\toprule |
| 70 |
|
|
$i$&$j$ & $r_0$ (\AA) & $k (\mathrm{~kcal/mole/\AA}^2)$ & source\\ |
| 71 |
|
|
\colrule |
| 72 |
|
|
\ce{CH3} & \ce{CH3} & 1.540 & 536 & \\ |
| 73 |
|
|
\ce{CH3} & \ce{CH2} & 1.540 & 536 & \\ |
| 74 |
|
|
\ce{CH3} & \ce{CH} & 1.540 & 536 & \\ |
| 75 |
|
|
\ce{CH2} & \ce{CH2} & 1.540 & 536 & \\ |
| 76 |
|
|
\ce{CH2} & \ce{CH} & 1.540 & 536 & \\ |
| 77 |
|
|
\ce{CH} & \ce{CH} & 1.540 & 536 & \\ |
| 78 |
|
|
\ce{CHene} & \ce{CHene} & 1.330 & 1098 & \\ |
| 79 |
|
|
\ce{CH2ene} & \ce{CHene} & 1.330 & 1098 & \\ |
| 80 |
|
|
\ce{CH3} & \ce{CHene} & 1.540 & 634 & \\ |
| 81 |
|
|
\ce{CH2} & \ce{CHene} & 1.540 & 634 & \\ |
| 82 |
|
|
S & \ce{CH2} & 1.820 & 444 & \\ |
| 83 |
|
|
\ce{CHar} & \ce{CHar} & 1.40 & 938 & \\ |
| 84 |
|
|
\ce{CHar} & \ce{CH2} & 1.540 & 536 & \\ |
| 85 |
|
|
\ce{CHar} & \ce{CH3} & 1.540 & 536 & \\ |
| 86 |
|
|
\ce{CH2ar} & \ce{CHar} & 1.40 & 938 & |
| 87 |
|
|
\protect\cite{William-L.-Jorgensen:1996uq} \\ |
| 88 |
|
|
S & \ce{CHar} & 1.80384 & 527.951 & fit \\ |
| 89 |
|
|
\botrule |
| 90 |
|
|
\end{tabular} |
| 91 |
|
|
\end{table} |
| 92 |
|
|
|
| 93 |
|
|
|
| 94 |
gezelter |
4379 |
To describe the interactions between metal (Au) and non-metal atoms, |
| 95 |
|
|
potential energy terms were adapted from an adsorption study of alkyl |
| 96 |
|
|
thiols on gold surfaces by Vlugt, \textit{et |
| 97 |
|
|
al.}\cite{vlugt:cpc2007154} They fit an effective pair-wise |
| 98 |
|
|
Lennard-Jones form of potential parameters for the interaction between |
| 99 |
|
|
Au and pseudo-atoms CH$_x$ and S based on a well-established and |
| 100 |
|
|
widely-used effective potential of Hautman and Klein for the Au(111) |
| 101 |
|
|
surface.\cite{hautman:4994} |
| 102 |
|
|
|
| 103 |
|
|
Parameters not found in the TraPPE-UA force field for the |
| 104 |
|
|
intramolecular interactions of the conjugated and the penultimate |
| 105 |
|
|
alkenethiolate ligands were calculated using constrained geometry |
| 106 |
|
|
scans using the B3LYP functional~\cite{Becke:1993kq,Lee:1988qf} and |
| 107 |
|
|
the 6-31G(d,p) basis set. Structures were scanned starting at the |
| 108 |
|
|
minimum energy gas phase structure for small ($C_4$) ligands. Only |
| 109 |
|
|
one degree of freedom was constrained for any given scan -- all other |
| 110 |
|
|
atoms were allowed to minimize subject to that constraint. The |
| 111 |
|
|
resulting potential energy surfaces were fit to a harmonic potential |
| 112 |
|
|
for the bond stretching, |
| 113 |
|
|
\begin{equation} |
| 114 |
|
|
V_\mathrm{bond} = \frac{k_\mathrm{bond}}{2} \left( r - r_0 \right)^2, |
| 115 |
|
|
\end{equation} |
| 116 |
|
|
and angle bending potentials, |
| 117 |
|
|
\begin{equation} |
| 118 |
|
|
V_\mathrm{bend} = \frac{k_\mathrm{bend}}{2} \left(\theta - \theta_0\right)^2. |
| 119 |
|
|
\end{equation} |
| 120 |
|
|
Torsional potentials were fit to the TraPPE torsional function, |
| 121 |
|
|
\begin{equation} |
| 122 |
|
|
V_\mathrm{tor} = c_0 + c_1 \left(1 + \cos\phi \right) + c_2 \left(1 - \cos 2\phi \right) + c_3 \left(1 + \cos 3 \phi \right). |
| 123 |
|
|
\end{equation} |
| 124 |
skucera |
4375 |
|
| 125 |
gezelter |
4381 |
For the penultimate thiolate ligands, the model molecule used was |
| 126 |
|
|
2-Butene-1-thiol, for which one bend angle (\ce{S-CH2-CHene}) was |
| 127 |
|
|
scanned to fit an equilibrium angle and force constant, as well as one |
| 128 |
|
|
torsion (\ce{S-CH2-CHene-CHene}). The parameters for these two |
| 129 |
|
|
potentials also served as model for the longer conjugated thiolate |
| 130 |
|
|
ligands which require bend angle parameters for (\ce{S-CH2-CHar}) and |
| 131 |
|
|
torsion parameters for (\ce{S-CH2-CHar-CHar}). |
| 132 |
gezelter |
4379 |
|
| 133 |
gezelter |
4381 |
For the $C_4$ conjugated thiolate ligands, the model molecule for the |
| 134 |
|
|
quantum mechanical calculations was 1,3-Butadiene-1-thiol. This |
| 135 |
|
|
ligand required fitting one bond (\ce{S-CHar}), and one bend angle |
| 136 |
|
|
(\ce{S-CHar-CHar}). |
| 137 |
gezelter |
4379 |
|
| 138 |
gezelter |
4381 |
The geometries of the model molecules were optimized prior to |
| 139 |
|
|
performing the constrained angle scans, and the fit values for the |
| 140 |
|
|
bond, bend, and torsional parameters were in relatively good agreement |
| 141 |
|
|
with similar parameters already present in TraPPE. |
| 142 |
gezelter |
4379 |
|
| 143 |
|
|
|
| 144 |
|
|
\begin{table}[h] |
| 145 |
|
|
\centering |
| 146 |
|
|
\caption{Bend angle parameters. The central atom in the bend is atom $j$.\label{tab:bend}} |
| 147 |
|
|
\begin{tabular}{ ccc|lll } |
| 148 |
|
|
\toprule |
| 149 |
gezelter |
4376 |
$i$&$j$&$k$ & $\theta_0 (\degree)$ & $k (\mathrm{kcal/mole/rad}^2)$ & source\\ |
| 150 |
gezelter |
4379 |
\colrule |
| 151 |
gezelter |
4381 |
\ce{CH2} & \ce{CH2} & S & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
| 152 |
|
|
\ce{CH3} & \ce{CH2} & S & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
| 153 |
|
|
\ce{CH3} & \ce{CH2} & \ce{CH3} & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
| 154 |
|
|
\ce{CH3} & \ce{CH2} & \ce{CH2} & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
| 155 |
|
|
\ce{CH2} & \ce{CH2} & \ce{CH2} & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
| 156 |
|
|
\ce{CH3} & \ce{CH2} & \ce{CH} & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
| 157 |
|
|
\ce{CHene} & \ce{CHene} & \ce{CH3} & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
| 158 |
|
|
\ce{CHene} & \ce{CHene} & \ce{CHene} & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
| 159 |
|
|
\ce{CH2ene} & \ce{CHene} & \ce{CH3} & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
| 160 |
|
|
\ce{CHene} & \ce{CHene} & \ce{CH2} & 119.7 & 139.94& Ref. \protect\cite{Maerzke:2009qy}\\ |
| 161 |
|
|
\ce{CH2} & \ce{CH2} & \ce{CHene} & 114.0 & 124.20& Ref. \protect\cite{TraPPE-UA.thiols}\\ |
| 162 |
|
|
\ce{CHar} & \ce{CHar} & \ce{CHar} & 120.0 & 126.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
| 163 |
|
|
\ce{CHar} & \ce{CHar} & \ce{CH2} & 120.0 & 140.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
| 164 |
|
|
\ce{CHar} & \ce{CHar} & \ce{CH3} & 120.0 & 140.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
| 165 |
|
|
\ce{CHar} & \ce{CHar} & \ce{CH2ar} & 120.0 & 126.0 & Refs. \protect\cite{Maerzke:2009qy} and \\ |
| 166 |
|
|
S & \ce{CH2} & \ce{CHene} & 109.97 & 127.37 & fit \\ |
| 167 |
|
|
S & \ce{CH2} & \ce{CHar} & 109.97 & 127.37 & fit \\ |
| 168 |
|
|
S & \ce{CHar} & \ce{CHar} & 123.911 & 138.093 & fit \\ |
| 169 |
gezelter |
4379 |
\botrule |
| 170 |
skucera |
4375 |
\end{tabular} |
| 171 |
gezelter |
4379 |
\end{table} |
| 172 |
|
|
|
| 173 |
|
|
\begin{table}[h] |
| 174 |
|
|
\centering |
| 175 |
gezelter |
4381 |
\caption{Torsion parameters. The central atoms for each torsion are atoms $j$ and $k$, |
| 176 |
|
|
and wildcard atom types are denoted by ``X''. All $c_n$ parameters |
| 177 |
|
|
have units of kcal/mol. The torsions around doubly-bonded carbons |
| 178 |
|
|
are harmonic and assume a trans (180$\degree$) geometry. The force |
| 179 |
|
|
constant for this torsion is given in $\mathrm{kcal~mol~}^{-1}\mathrm{degrees}^{-2}$. \label{tab:torsion}} |
| 180 |
gezelter |
4379 |
\begin{tabular}{ cccc|lllll } |
| 181 |
|
|
\toprule |
| 182 |
|
|
$i$&$j$&$k$&$l$& $c_0$&$c_1$& $c_2$ & $c_3$ & source\\ |
| 183 |
|
|
\colrule |
| 184 |
gezelter |
4381 |
\ce{CH3} & \ce{CH2} & \ce{CH2} & \ce{CH3} & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
| 185 |
|
|
\ce{CH3} & \ce{CH2} & \ce{CH2} & \ce{CH2} & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
| 186 |
|
|
\ce{CH3} & \ce{CH2} & \ce{CH2} & \ce{CH} & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
| 187 |
|
|
\ce{CH2} & \ce{CH2} & \ce{CH2} & \ce{CH2} & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
| 188 |
|
|
\ce{CH2} & \ce{CH2} & \ce{CH2} & S & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
| 189 |
|
|
\ce{CH3} & \ce{CH2} & \ce{CH2} & S & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ \colrule |
| 190 |
|
|
X & \ce{CHene} & \ce{CHene} & X & \multicolumn{4}{c}{\multirow{2}{*}{$V = \frac{0.008112}{2} (\phi - 180.0)^2$}} & \multirow{2}{*}{Ref. \protect\cite{TraPPE-UA.alkylbenzenes}} \\ |
| 191 |
|
|
X & \ce{CHar} & \ce{CHar} & X & & & & & \\ \colrule |
| 192 |
|
|
\ce{CH2} & \ce{CH2} & \ce{CHene} & \ce{CHene} & 1.368 & 0.1716 & -0.2181 & -0.56081 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
| 193 |
|
|
\ce{CH2} & \ce{CH2} & \ce{CH2} & \ce{CHene} & 0.0 & 0.7055 & -0.13551 & 1.5725 & Ref. \protect\cite{TraPPE-UA.alkylbenzenes}\\ |
| 194 |
|
|
\ce{CHene} & \ce{CHene} & \ce{CH2} & S & 3.20753 & 0.207417& -0.912929& -0.958538 & fit \\ |
| 195 |
|
|
\ce{CHar} & \ce{CHar} & \ce{CH2} & S & 3.20753 & 0.207417& -0.912929& -0.958538 & fit \\ |
| 196 |
gezelter |
4379 |
\botrule |
| 197 |
skucera |
4375 |
\end{tabular} |
| 198 |
gezelter |
4379 |
\end{table} |
| 199 |
skucera |
4378 |
|
| 200 |
gezelter |
4379 |
\begin{table}[h] |
| 201 |
|
|
\centering |
| 202 |
|
|
\caption{Non-bonded cross interaction parameters between gold atoms and the united atom sites\label{tab:nb}} |
| 203 |
|
|
\begin{tabular}{ cc|ccc } |
| 204 |
|
|
\toprule |
| 205 |
|
|
$i$&$j$ & $\sigma$ (\AA)& $\epsilon$ $(kcal/mol)$ & source \\ |
| 206 |
|
|
\colrule |
| 207 |
gezelter |
4381 |
Au &\ce{CH3} &3.54 &0.2146& Ref. \protect\cite{vlugt:cpc2007154}\\ |
| 208 |
|
|
Au &\ce{CH2} &3.54 &0.1749& Ref. \protect\cite{vlugt:cpc2007154}\\ |
| 209 |
|
|
Au &\ce{CHene} &3.4625 &0.1680& Ref. \protect\cite{vlugt:cpc2007154}\\ |
| 210 |
|
|
Au &\ce{CHar} &3.4625 &0.1680& Ref. \protect\cite{vlugt:cpc2007154}\\ |
| 211 |
|
|
Au &\ce{CH2ar} &3.4625 &0.1680& Ref. \protect\cite{vlugt:cpc2007154}\\ |
| 212 |
gezelter |
4379 |
Au &S &2.40 &8.465& Ref. \protect\cite{vlugt:cpc2007154}\\ |
| 213 |
|
|
\botrule |
| 214 |
skucera |
4378 |
\end {tabular} |
| 215 |
gezelter |
4379 |
\end{table} |
| 216 |
gezelter |
4376 |
\newpage |
| 217 |
|
|
\bibliographystyle{aip} |
| 218 |
|
|
\bibliography{NPthiols} |
| 219 |
|
|
|
| 220 |
skucera |
4375 |
\end{document} |
