[ViewVC] Diff of: group/trunk/chainLength/GoldThiolsPaper.tex

Comparing trunk/chainLength/GoldThiolsPaper.tex (file contents):
Revision 3802 by kstocke1, Wed Dec 5 16:34:23 2012 UTC vs.
Revision 3803 by gezelter, Wed Dec 5 21:49:28 2012 UTC

+\begin{document}
-<
+\title{Interfacial Thermal Conductance of Thiolate-Capped Gold}
->
+\title{The role chain length and solvent penetration in the
->
+  interfacial thermal conductance of thiolate-capped gold surfaces}
-<
+\author{Kelsey M. Stocker and J. Daniel Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\
->
+\author{Kelsey M. Stocker and J. Daniel
->
+  Gezelter\footnote{Corresponding author. \ Electronic mail:
->
+    gezelter@nd.edu} \\
->
+Nieuwland Science Hall, \\
+        Department of Chemistry and Biochemistry,\\
+        University of Notre Dame\\
+        Notre Dame, Indiana 46556}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Introduction}
-+
+The structural and dynamical details of interfaces between metal
-+
+nanoparticles and solvents determines how energy flows between these
-+
+particles and their surroundings. Understanding this energy flow is
-+
+essential in designing and functionalizing metallic nanoparticles for
-+
+plasmonic photothermal
-+
+therapies,\cite{Jain:2007ux,Petrova:2007ad,Gnyawali:2008lp,Mazzaglia:2008to,Huff
-+
+  :2007ye,Larson:2007hw} which rely on the ability of metallic
-+
+nanoparticles to absorb light in the near-IR, a portion of the
-+
+spectrum in which living tissue is very nearly transparent.  The
-+
+principle of this therapy is to pump the particles at high power at
-+
+the plasmon resonance and to allow heat dissipation to kill targeted
-+
+(e.g. cancerous) cells.  The relevant physical property controlling
-+
+this transfer of energy is the interfacial thermal conductance, $G$,
-+
+which can be somewhat difficult to determine
-+
+experimentally.\cite{Wilson:2002uq,Plech:2005kx}
-+
-+
+Metallic particles have also been proposed for use in highly efficient
-+
+thermal-transfer fluids, although careful experiments by Eapen {\it et al.}
-+
+have shown that metal-particle-based ``nanofluids'' have thermal
-+
+conductivities that match Maxwell predictions.\cite{Eapen:2007th} The
-+
+likely cause of previously reported non-Maxwell
-+
+behavior\cite{Eastman:2001wb,Keblinski:2002bx,Lee:1999ct,Xue:2003ya,Xue:2004oa}
-+
+is percolation networks of nanoparticles exchanging energy via the
-+
+solvent,\cite{Eapen:2007mw} so it is vital to get a detailed molecular
-+
+picture of particle-solvent interactions in order to understand the
-+
+thermal behavior of complex fluids. To date, there have been few
-+
+reported values (either from theory or experiment) for $G$ for
-+
+ligand-protected nanoparticles embedded in liquids, and there is a
-+
+significant gap in knowledge about how chemically distinct ligands or
-+
+protecting groups will affect heat transport from the particles.
-+
-+
+The thermal properties of various nanostructured interfaces have been
-+
+investigated experimentally by a number of groups: Cahill and
-+
+coworkers studied nanoscale thermal transport from metal
-+
+nanoparticle/fluid interfaces, to epitaxial TiN/single crystal oxides
-+
+interfaces, and hydrophilic and hydrophobic interfaces between water
-+
+and solids with different self-assembled
-+
+monolayers.\cite{cahill:793,Wilson:2002uq,PhysRevB.67.054302,doi:10.1021/jp048375k,PhysRevL
-+
+ett.96.186101}
-+
+Wang {\it et al.} studied heat transport through long-chain
-+
+hydrocarbon monolayers on gold substrate at the individual molecular
-+
+level,\cite{Wang10082007} Schmidt {\it et al.} studied the role of
-+
+cetyltrimethylammonium bromide (CTAB) on the thermal transport between
-+
+gold nanorods and solvent,\cite{doi:10.1021/jp8051888} and Juv\'e {\it
-+
+  et al.} studied the cooling dynamics, which is controlled by thermal
-+
+interface resistance of glass-embedded metal
-+
+nanoparticles.\cite{PhysRevB.80.195406} Although interfaces are
-+
+normally considered barriers for heat transport, Alper {\it et al.}
-+
+suggested that specific ligands (capping agents) could completely
-+
+eliminate this barrier
-+
+($G\rightarrow\infty$).\cite{doi:10.1021/la904855s}
-+
-+
+In previous simulations, we applied a variant of reverse
-+
+non-equilibrium molecular dynamics (RNEMD) to calculate the
-+
+interfacial thermal conductance at a metal / organic solvent interface
-+
+that had been chemically protected by butanethiolate groups.  Our
-+
+calculations suggest an explanation for the very large thermal
-+
+conductivity at alkanethiol-capped metal surfaces when compared with
-+
+bare metal/solvent interfaces.  Specifically, the chemical bond
-+
+between the metal and the ligand introduces a vibrational overlap that
-+
+is not present without the protecting group, and the overlap between
-+
+the vibrational spectra (metal to ligand, ligand to solvent) provides
-+
+a mechanism for rapid thermal transport across the interface.
-+
-+
+One interesting result of our previous work was the observation of
-+
+{\it non-monotonic dependence} of the thermal conductance on the
-+
+coverage of a metal surface by a chemical protecting group.  Our
-+
+explanation for this behavior was that gaps in surface coverage
-+
+allowed solvent to penetrate close to the capping molecules that had
-+
+been heated by the metal surface, to absorb thermal energy from these
-+
+molecules, and then diffuse away.  The effect of surface coverage is
-+
+relatively difficult to study as the individual protecting groups have
-+
+lateral mobility on the surface and can aggregate to form domains on
-+
+the timescale of the simulation.
-+
-+
+The work reported here involves the use of velocity shearing and
-+
+scaling reverse non-equilibrium molecular dynamics (VSS-RNEMD) to
-+
+study surfaces composed of mixed-length chains which collectively form
-+
+a complete monolayer on the surfaces.  These complete (but
-+
+mixed-chain) surfaces are significantly less prone to surface domain
-+
+formation, and would allow us to further investigate the mechanism of
-+
+heat transport to the solvent.
-+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%                          **METHODOLOGY**
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Methodology}
-+
+There are many ways to compute bulk transport properties from
-+
+classical molecular dynamics simulations.  Equilibrium Molecular
-+
+Dynamics (EMD) simulations can be used by computing relevant time
-+
+correlation functions and assuming that linear response theory
-+
+holds.\cite{PhysRevB.37.5677,MASSOBRIO:1984bl,PhysRev.119.1,Viscardy:2007rp,che:6888,kinaci:014106}
-+
+For some transport properties (notably thermal conductivity), EMD
-+
+approaches are subject to noise and poor convergence of the relevant
-+
+correlation functions. Traditional Non-equilibrium Molecular Dynamics
-+
+(NEMD) methods impose a gradient (e.g. thermal or momentum) on a
-+
+simulation.\cite{ASHURST:1975tg,Evans:1982zk,ERPENBECK:1984sp,MAGINN:1993hc,Berthier:2002ij,Evans:2002ai,Schelling:2002dp,PhysRevA.34.1449,JiangHao_jp802942v}
-+
+However, the resulting flux is often difficult to
-+
+measure. Furthermore, problems arise for NEMD simulations of
-+
+heterogeneous systems, such as phase-phase boundaries or interfaces,
-+
+where the type of gradient to enforce at the boundary between
-+
+materials is unclear.
-+
-+
+{\it Reverse} Non-Equilibrium Molecular Dynamics (RNEMD) methods adopt
-+
+a different approach in that an unphysical {\it flux} is imposed
-+
+between different regions or ``slabs'' of the simulation
-+
+box.\cite{MullerPlathe:1997xw,ISI:000080382700030,Kuang:2010uq} The
-+
+system responds by developing a temperature or momentum {\it gradient}
-+
+between the two regions. Since the amount of the applied flux is known
-+
+exactly, and the measurement of a gradient is generally less
-+
+complicated, imposed-flux methods typically take shorter simulation
-+
+times to obtain converged results for transport properties.  The
-+
+corresponding temperature or velocity gradients which develop in
-+
+response to the applied flux are then related (via linear response
-+
+theory) to the transport coefficient of interest.  These methods are
-+
+quite efficient, in that they do not need many trajectories to provide
-+
+information about transport properties. To date, they have been
-+
+utilized in computing thermal and mechanical transfer of both
-+
+homogeneous
-+
+liquids~\cite{MullerPlathe:1997xw,ISI:000080382700030,Maginn:2010} as
-+
+well as heterogeneous
-+
+systems.\cite{garde:nl2005,garde:PhysRevLett2009,kuang:AuThl}
-+
+        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+        %                           VSS-RNEMD
+        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+        \subsection{VSS-RNEMD}
-<
->
+The original ``swapping'' approaches by M\"{u}ller-Plathe {\it et
->
+  al.}\cite{ISI:000080382700030,MullerPlathe:1997xw} can be understood
->
+as a sequence of imaginary elastic collisions between particles in
->
+regions separated by half of the simulation cell.  In each collision,
->
+the entire momentum vectors of both particles may be exchanged to
->
+generate a thermal flux. Alternatively, a single component of the
->
+momentum vectors may be exchanged to generate a shear flux.  This
->
+algorithm turns out to be quite useful in many simulations of bulk
->
+liquids. However, the M\"{u}ller-Plathe swapping approach perturbs the
->
+system away from ideal Maxwell-Boltzmann distributions, and this has
->
+undesirable side-effects when the applied flux becomes
->
+large.\cite{Maginn:2010}
->
->
+Instead of having momentum exchange between {\it individual particles}
->
+in each slab, the NIVS algorithm applies velocity scaling to all of
->
+the selected particles in both slabs.\cite{Kuang:2010uq} A combination
->
+of linear momentum, kinetic energy, and flux constraint equations
->
+governs the amount of velocity scaling performed at each step.  NIVS
->
+has been shown to be very effective at producing thermal gradients and
->
+for computing thermal conductivities, particularly for heterogeneous
->
+interfaces.  Although the NIVS algorithm can also be applied to impose
->
+a directional momentum flux, thermal anisotropy was observed in
->
+relatively high flux simulations, and the method is not suitable for
->
+imposing a shear flux or for computing shear viscosities.
->
->
+The most useful RNEMD
->
+approach developed so far utilizes a series of simultaneous velocity
->
+shearing and scaling exchanges between the two
->
+slabs.\cite{2012MolPh.110..691K} This method provides a set of
->
+conservation constraints while simultaneously creating a desired flux
->
+between the two slabs.  Satisfying the constraint equations ensures
->
+that the new configurations are sampled from the same NVE ensemble.
->
->
+The VSS moves are applied periodically to scale and shift the particle
->
+velocities ($\mathbf{v}_i$ and $\mathbf{v}_j$) in two slabs ($H$ and
->
+$C$) which are separated by half of the simulation box,
->
+\begin{displaymath}
->
+\begin{array}{rclcl}
->
->
+ & \underline{\mathrm{shearing}} & &
->
+ \underline{~~~~~~~~~~~~\mathrm{scaling}~~~~~~~~~~~~} \\  \\
->
+\mathbf{v}_i \leftarrow &
->
+  \mathbf{a}_c\ & + & c\cdot\left(\mathbf{v}_i - \langle\mathbf{v}_c
->
+  \rangle\right)  +  \langle\mathbf{v}_c\rangle \\
->
+\mathbf{v}_j \leftarrow &
->
+  \mathbf{a}_h & + & h\cdot\left(\mathbf{v}_j - \langle\mathbf{v}_h
->
+    \rangle\right) + \langle\mathbf{v}_h\rangle .
->
->
+\end{array}
->
+\end{displaymath}
->
+Here $\langle\mathbf{v}_c\rangle$ and $\langle\mathbf{v}_h\rangle$ are
->
+the center of mass velocities in the $C$ and $H$ slabs, respectively.
->
+Within the two slabs, particles receive incremental changes or a
->
+``shear'' to their velocities.  The amount of shear is governed by the
->
+imposed momentum flux, $j_z(\mathbf{p})$
->
+\begin{eqnarray}
->
+\mathbf{a}_c & = & - \mathbf{j}_z(\mathbf{p}) \Delta t / M_c \label{vss1}\\
->
+\mathbf{a}_h & = & + \mathbf{j}_z(\mathbf{p}) \Delta t / M_h \label{vss2}
->
+\end{eqnarray}
->
+where $M_{\{c,h\}}$ is total mass of particles within each slab and $\Delta t$
->
+is the interval between two separate operations.
->
->
+To simultaneously impose a thermal flux ($J_z$) between the slabs we
->
+use energy conservation constraints,
->
+\begin{eqnarray}
->
+K_c - J_z\Delta t & = & c^2 (K_c - \frac{1}{2}M_c \langle\mathbf{v}_c
->
+\rangle^2) + \frac{1}{2}M_c (\langle \mathbf{v}_c \rangle + \mathbf{a}_c)^2 \label{vss3}\\
->
+K_h + J_z\Delta t & = & h^2 (K_h - \frac{1}{2}M_h \langle\mathbf{v}_h
->
+\rangle^2) + \frac{1}{2}M_h (\langle \mathbf{v}_h \rangle +
->
+\mathbf{a}_h)^2 \label{vss4}.
->
+\label{constraint}
->
+\end{eqnarray}
->
+Simultaneous solution of these quadratic formulae for the scaling
->
+coefficients, $c$ and $h$, will ensure that the simulation samples from
->
+the original microcanonical (NVE) ensemble.  Here $K_{\{c,h\}}$ is the
->
+instantaneous translational kinetic energy of each slab.  At each time
->
+interval, it is a simple matter to solve for $c$, $h$, $\mathbf{a}_c$,
->
+and $\mathbf{a}_h$, subject to the imposed momentum flux,
->
+$j_z(\mathbf{p})$, and thermal flux, $J_z$ values.  Since the VSS
->
+operations do not change the kinetic energy due to orientational
->
+degrees of freedom or the potential energy of a system, configurations
->
+after the VSS move have exactly the same energy ({\it and} linear
->
+momentum) as before the move.
->
->
+As the simulation progresses, the VSS moves are performed on a regular
->
+basis, and the system develops a thermal or velocity gradient in
->
+response to the applied flux.  Using the slope of the temperature or
->
+velocity gradient, it is quite simple to obtain of thermal
->
+conductivity ($\lambda$),
->
+\begin{equation}
->
+J_z = -\lambda \frac{\partial T}{\partial z},
->
+\end{equation}
->
+and shear viscosity ($\eta$),
->
+\begin{equation}
->
+j_z(p_x) = -\eta \frac{\partial \langle v_x \rangle}{\partial z}.
->
+\end{equation}
->
+Here, the quantities on the left hand side are the imposed flux
->
+values, while the slopes are obtained from linear fits to the
->
+gradients that develop in the simulated system.
->
->
+The VSS-RNEMD approach is versatile in that it may be used to
->
+implement both thermal and shear transport either separately or
->
+simultaneously.  Perturbations of velocities away from the ideal
->
+Maxwell-Boltzmann distributions are minimal, and thermal anisotropy is
->
+kept to a minimum.  This ability to generate simultaneous thermal and
->
+shear fluxes has been previously utilized to map out the shear
->
+viscosity of SPC/E water over a wide range of temperatures (90~K) with
->
+a {\it single 1 ns simulation}.\cite{2012MolPh.110..691K}
->
+        \begin{figure}
+                \includegraphics[width=\linewidth]{figures/rnemd}
+                \caption{VSS-RNEMD}
+                \label{fig:rnemd}
+        \end{figure}
-–
+        \begin{equation}
-–
+                \boldsymbol{\nu}_{i} \leftarrow c \cdot \left( \boldsymbol{\nu}_{i} - \langle \boldsymbol{\nu}_{c} \rangle \right) + \left( \langle \boldsymbol{\nu}_{c} \rangle + \bold{a}_{c} \right),
-–
+        \end{equation}
-–
+        \begin{equation}
-–
+                \boldsymbol{\nu}_{j} \leftarrow h \cdot \left( \boldsymbol{\nu}_{j} - \langle \boldsymbol{\nu}_{h} \rangle \right) + \left( \langle \boldsymbol{\nu}_{h} \rangle + \bold{a}_{h} \right),
-–
+        \end{equation}
-–
+        \begin{equation}
-–
+                K_{c} - J_{z} \Delta t = c^{2} \left( K_{c} - \frac{1}{2} M_{c} \langle \boldsymbol{\nu}_{c} \rangle ^{2}  \right) + \frac{1}{2} M_{c} \left( \langle \boldsymbol{\nu}_{c} \rangle + \bold{a}_{c} \right) ^{2},
-–
+        \end{equation}
-–
-–
+        \begin{equation}
-–
+                K_{h} + J_{z} \Delta t = h^{2} \left( K_{h} - \frac{1}{2} M_{h} \langle \boldsymbol{\nu}_{h} \rangle ^{2}  \right) + \frac{1}{2} M_{h} \left( \langle \boldsymbol{\nu}_{h} \rangle + \bold{a}_{h} \right) ^{2},
-–
+        \end{equation}
-–
-–
-–
+        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+        %                          INTERFACIAL CONDUCTANCE
+        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-<
+        \subsection{Defining Interfacial Conductance (G)}
-<
-<
+        \begin{figure}
-<
+                \includegraphics[width=\linewidth]{figures/resistor_series}
-<
+                \caption{RESISTOR SERIES}
-<
+                \label{fig:resistor_series}
-<
+        \end{figure}
-<
-<
-<
+There are two interfaces involved in the transfer of heat from the gold slab to the solvent: the gold/thiolate interface and the thiolate/solvent interface. We can treat the temperature on each side of an interface as discrete, making the interfacial conductance the inverse of the Kaptiza resistance, or $G = \frac{J}{\Delta T}$. To model the total conductance across multiple interfaces, we treat the interfaces as resistors in series. Resistors in series are additive, ($R_{total} = R_{1} + R_{2} + R_{3} + ...$) and the total conductance is the inverse of the total resistance, or $G = \frac{1}{(R_{1} + R_{2} + R_{3} + ...}$). We treat each bin in the VSS-RNEMD temperature profile as a resistor with resistance $\frac{T_{2}-T_{1}}{J}$, $\frac{T_{3}-T_{2}}{J}$, etc. The sum of this resistor series which spans the gold/thiolate interface, thiolate chains, and thiolate/solvent interface simplifies to
->
+        \subsection{Reverse Non-Equilibrium Molecular Dynamics approaches
->
+  to interfacial transport}
-<
+\begin{equation}
-<
+        \frac{T_{n}-T_{1}}{J},
-<
+        \label{eq:finalG}
-<
+        \end{equation}
->
+Interfaces between dissimilar materials have transport properties
->
+which can be defined as derivatives of the standard transport
->
+coefficients in a direction normal to the interface. For example, the
->
+{\it interfacial} thermal conductance ($G$) can be thought of as the
->
+change in the thermal conductivity ($\lambda$) across the boundary
->
+between materials:
->
+\begin{align}
->
+  G &= \left(\nabla\lambda \cdot \mathbf{\hat{n}}\right)_{z_0} \\
->
+  &= J_z\left(\frac{\partial^2 T}{\partial z^2}\right)_{z_0} \Big/
->
+  \left(\frac{\partial T}{\partial z}\right)_{z_0}^2.
->
+  \label{derivativeG}
->
+\end{align}
->
+where $z_0$ is the location of the interface between two materials and
->
+$\mathbf{\hat{n}}$ is a unit vector normal to the interface (assumed
->
+to be the $z$ direction from here on).  RNEMD simulations, and
->
+particularly the VSS-RNEMD approach, function by applying a momentum
->
+or thermal flux and watching the gradient response of the
->
+material. This means that the {\it interfacial} conductance is a
->
+second derivative property which is subject to significant noise and
->
+therefore requires extensive sampling.  We have been able to
->
+demonstrate the use of the second derivative approach to compute
->
+interfacial conductance at chemically-modified metal / solvent
->
+interfaces.  However, a definition of the interfacial conductance in
->
+terms of a temperature difference ($\Delta T$) measured at $z_0$,
->
+\begin{displaymath}
->
+G = \frac{J_z}{\Delta T_{z_0}},
->
+\end{displaymath}
->
+is useful once the RNEMD approach has generated a stable temperature
->
+gap across the interface.
-<
+or the temperature difference between the gold side of the gold/thiolate interface and the solvent side of the thiolate/solvent interface over the applied flux.
->
+\begin{figure}
->
+  \includegraphics[width=\linewidth]{figures/resistor_series}
->
+  \caption{RESISTOR SERIES}
->
+  \label{fig:resistor_series}
->
+\end{figure}
->
->
+In the particular case we are studying here, there are two interfaces
->
+involved in the transfer of heat from the gold slab to the solvent:
->
+the gold/thiolate interface and the thiolate/solvent interface. We
->
+could treat the temperature on each side of an interface as discrete,
->
+making the interfacial conductance the inverse of the Kaptiza
->
+resistance, or $G = \frac{1}{R_k}$. To model the total conductance
->
+across multiple interfaces, it is useful to think of the interfaces as
->
+a set of resistors wired in series. The total resistance is then
->
+additive, $R_{total} = \sum_i R_{i}$ and the interfacial conductance
->
+is the inverse of the total resistance, or $G = \frac{1}{\sum_i
->
+  R_i}$).  In the interfacial region, we treat each bin in the
->
+VSS-RNEMD temperature profile as a resistor with resistance
->
+$\frac{T_{2}-T_{1}}{J_z}$, $\frac{T_{3}-T_{2}}{J_z}$, etc.  The sum of
->
+the set of resistors which spans the gold/thiolate interface, thiolate
->
+chains, and thiolate/solvent interface simplifies to
->
+\begin{equation}
->
+  \frac{T_{n}-T_{1}}{J_z},
->
+  \label{eq:finalG}
->
+\end{equation}
->
+or the temperature difference between the gold side of the
->
+gold/thiolate interface and the solvent side of the thiolate/solvent
->
+interface over the applied flux.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Computational Details}
-<
+        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-<
+        %                          SIMULATION PROTOCOL
-<
+        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-<
+        \subsection{Simulation Protocol}
-<
-<
+We have implemented the VSS-RNEMD algorithm in OpenMD, our group molecular dynamics code. A gold slab 11 layers thick was equilibrated at 1 atm and 200 K. The periodic box was expanded in the z direction to expose two Au(111) faces.
->
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
->
+% SIMULATION PROTOCOL
->
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
->
+\subsection{Simulation Protocol}
-+
+We have implemented the VSS-RNEMD algorithm in OpenMD, our
-+
+group molecular dynamics code. A gold slab 11 atoms thick was
-+
+equilibrated at 1 atm and 200 K. The periodic box was expanded
-+
+in the z direction to expose two Au(111) faces.
-+
+A full monolayer of thiolates (1/3 the number of surface gold atoms) was placed on three-fold hollow sites on the gold interfaces. To efficiently test the effect of thiolate binding sites on the thermal conductance, all systems had one gold interface with thiolates placed only on fcc hollow sites and the other interface with thiolates only on hcp hollow sites. To test the effect of thiolate chain length on interfacial thermal conductance, full coverages of five chain lengths were tested: butanethiolate, hexanethiolate, octanethiolate, decanethiolate, and dodecanethiolate. To test the effect of mixed chain lengths, full coverages of butanethiolate/decanethiolate and butanethiolate/dodecanethiolate mixtures were created in short/long chain ratios of 25/75, 50/50, and 75/25. The short and long chains were placed on the surface in a random configuration.
+The simulation box z dimension was set to roughly double the length of the gold/thiolate block. Solvent molecules were placed in the vacant portion of the box using the packmol algorithm. Two solvent molecules were examined: hexane and toluene. Hexane, a straight chain flexible alkane, is very structurally similar to the thiolate alkane tails while toluene is a rigid planar molecule.

Diff Legend

-–
+Removed lines
-+
+Added lines
-<
+Changed lines
->
+Changed lines

Comparing trunk/chainLength/GoldThiolsPaper.tex (file contents): Revision 3802 by kstocke1, Wed Dec 5 16:34:23 2012 UTC vs. Revision 3803 by gezelter, Wed Dec 5 21:49:28 2012 UTC

Diff Legend

Comparing trunk/chainLength/GoldThiolsPaper.tex (file contents):
Revision 3802 by kstocke1, Wed Dec 5 16:34:23 2012 UTC vs.
Revision 3803 by gezelter, Wed Dec 5 21:49:28 2012 UTC