| 50 |
|
protein simulation |
| 51 |
|
community.\cite{BROOKS:1985kx,BROOKS:1983uq,BRUNGER:1984fj} A sketch |
| 52 |
|
of this setup can be found in Fig. \ref{fig:langevinSketch}. In |
| 53 |
< |
equation \ref{eq:langevin} the frictional forces of a spherical atom |
| 53 |
> |
Eq. (\ref{eq:langevin}) the frictional forces of a spherical atom |
| 54 |
|
of radius $a$ depend on the solvent viscosity. The random forces are |
| 55 |
|
usually taken as gaussian random variables with zero mean and a |
| 56 |
|
variance tied to the solvent viscosity and temperature, |
| 113 |
|
\end{equation} |
| 114 |
|
For simplicity, we have introduced the thermal diffusivity $\kappa = |
| 115 |
|
K/(\rho c)$, and defined $k=4\pi R^3 \rho c /(M c_p)$ and $g = G/K$ in |
| 116 |
< |
Eq. \ref{eq:laplacetransform}. |
| 116 |
> |
Eq. (\ref{eq:laplacetransform}). |
| 117 |
|
|
| 118 |
< |
Eq. \ref{eq:laplacetransform} was solved numerically for the Ag-Cu |
| 118 |
> |
Eq. (\ref{eq:laplacetransform}) was solved numerically for the Ag-Cu |
| 119 |
|
system using mole-fraction weighted values for $c_p$ and $\rho_p$ of |
| 120 |
|
0.295 $(\mathrm{J g^{-1} K^{-1}})$ and $9.826\times 10^6$ $(\mathrm{g |
| 121 |
|
m^{-3}})$ respectively. Since most of the laser excitation experiments |
| 126 |
|
Values for the interfacial conductance have been determined by a |
| 127 |
|
number of groups for similar nanoparticles and range from a low |
| 128 |
|
$87.5\times 10^{6} (\mathrm{Wm^{-2}K^{-1}})$ to $130\times 10^{6} |
| 129 |
< |
(\mathrm{Wm^{-2}K^{-1}})$.\cite{XXXHartland,Wilson:2002uq} Wilson {\it |
| 129 |
> |
(\mathrm{Wm^{-2}K^{-1}})$.\cite{Wilson:2002uq} Wilson {\it |
| 130 |
|
et al.} worked with Au, Pt, and AuPd nanoparticles and obtained an |
| 131 |
|
estimate for the interfacial conductance of $G=130 |
| 132 |
|
(\mathrm{Wm^{-2}K^{-1}})$.\cite{Wilson:2002uq} Similarly, Plech {\it |
| 149 |
|
The rate of cooling for the nanoparticles in a molecular dynamics |
| 150 |
|
simulation can then be tuned by changing the effective solvent |
| 151 |
|
viscosity ($\eta$) until the nanoparticle cooling rate matches the |
| 152 |
< |
cooling rate described by the heat-transfer equations |
| 152 |
> |
cooling rate described by the heat-transfer Eq. |
| 153 |
|
(\ref{eq:heateqn}). The effective solvent viscosity (in Pa s) for a G |
| 154 |
|
of $87.5\times 10^{6}$ $(\mathrm{Wm^{-2}K^{-1}})$ is $4.2 \times |
| 155 |
|
10^{-6}$, $5.0 \times 10^{-6}$, and |
| 172 |
|
Fig. \ref{fig:images_cooling_plot}. It should be noted that the |
| 173 |
|
Langevin thermostat produces cooling curves that are consistent with |
| 174 |
|
Newtonian (single-exponential) cooling, which cannot match the cooling |
| 175 |
< |
profiles from Eq. \ref{eq:laplacetransform} exactly. Fitting the |
| 175 |
> |
profiles from Eq. (\ref{eq:laplacetransform}) exactly. Fitting the |
| 176 |
|
Langevin cooling profiles to a single-exponential produces |
| 177 |
|
$\tau=25.576$ ps, $\tau=43.786$ ps, and $\tau=56.621$ ps for the 20, |
| 178 |
|
30 and 40 {\AA} nanoparticles and a G of $87.5\times 10^{6}$ |
| 186 |
|
\centering |
| 187 |
|
\includegraphics[width=5in]{images/cooling_plot.pdf} |
| 188 |
|
\caption{Thermal cooling curves obtained from the inverse Laplace |
| 189 |
< |
transform heat model in Eq. \ref{eq:laplacetransform} (solid line) as |
| 189 |
> |
transform heat model in Eq. (\ref{eq:laplacetransform}) (solid line) as |
| 190 |
|
well as from molecular dynamics simulations (circles). Effective |
| 191 |
|
solvent viscosities of 4.2-7.5 $\times 10^{-6}$ Pa s (depending on the |
| 192 |
|
radius of the particle) give the best fit to the experimental cooling |
| 252 |
|
nanoparticles throughout the cooling trajectory, configurations were |
| 253 |
|
sampled at regular intervals during the cooling trajectory. These |
| 254 |
|
configurations were then allowed to evolve under NVE dynamics to |
| 255 |
< |
sample from the proper distribution in phase space. Figure |
| 255 |
> |
sample from the proper distribution in phase space. Fig. |
| 256 |
|
\ref{fig:images_cooling_time_traces} illustrates this sampling. |
| 257 |
|
|
| 258 |
|
|
