| 146 |
|
simulation can then be tuned by changing the effective solvent |
| 147 |
|
viscosity ($\eta$) until the nanoparticle cooling rate matches the |
| 148 |
|
cooling rate described by the heat-transfer equations |
| 149 |
< |
(\ref{eq:heateqn}). The effective solvent viscosity (in poise) for a G |
| 150 |
< |
of $87.5\times 10^{6}$ $(\mathrm{Wm^{-2}K^{-1}})$ is 0.17, 0.20, and |
| 151 |
< |
0.22 for 20 {\AA}, 30 {\AA}, and 40 {\AA} particles, respectively. The |
| 152 |
< |
effective solvent viscosity (again in poise) for an interfacial |
| 153 |
< |
conductance of $117\times 10^{6}$ $(\mathrm{Wm^{-2}K^{-1}})$ is 0.23, |
| 154 |
< |
0.29, and 0.30 for 20 {\AA}, 30 {\AA} and 40 {\AA} particles. Cooling |
| 155 |
< |
traces for each particle size are presented in |
| 149 |
> |
(\ref{eq:heateqn}). The effective solvent viscosity (in Pa s) for a G |
| 150 |
> |
of $87.5\times 10^{6}$ $(\mathrm{Wm^{-2}K^{-1}})$ is $4.2 \times |
| 151 |
> |
10^{-6}$, $5.0 \times 10^{-6}$, and |
| 152 |
> |
$5.5 \times 10^{-6}$ for 20 {\AA}, 30 {\AA}, and 40 {\AA} particles, respectively. The |
| 153 |
> |
effective solvent viscosity (again in Pa s) for an interfacial |
| 154 |
> |
conductance of $117\times 10^{6}$ $(\mathrm{Wm^{-2}K^{-1}})$ is $5.7 |
| 155 |
> |
\times 10^{-6}$, $7.2 \times 10^{-6}$, and $7.5 \times 10^{-6}$ |
| 156 |
> |
for 20 {\AA}, 30 {\AA} and 40 {\AA} particles. Cooling traces for |
| 157 |
> |
each particle size are presented in |
| 158 |
|
Fig. \ref{fig:images_cooling_plot}. It should be noted that the |
| 159 |
|
Langevin thermostat produces cooling curves that are consistent with |
| 160 |
|
Newtonian (single-exponential) cooling, which cannot match the cooling |
| 174 |
|
\caption{Thermal cooling curves obtained from the inverse Laplace |
| 175 |
|
transform heat model in Eq. \ref{eq:laplacetransform} (solid line) as |
| 176 |
|
well as from molecular dynamics simulations (circles). Effective |
| 177 |
< |
solvent viscosities of 0.23-0.30 poise (depending on the radius of the |
| 178 |
< |
particle) give the best fit to the experimental cooling curves. |
| 179 |
< |
%Since |
| 180 |
< |
%this viscosity is substantially in excess of the viscosity of liquid |
| 181 |
< |
%water, much of the thermal transfer to the surroundings is probably |
| 180 |
< |
%due to the capping agent. |
| 181 |
< |
} |
| 177 |
> |
solvent viscosities of 4.2-7.5 $\times 10^{-6}$ Pa s (depending on the |
| 178 |
> |
radius of the particle) give the best fit to the experimental cooling |
| 179 |
> |
curves. This viscosity suggests that the nanoparticles in these |
| 180 |
> |
experiments are surrounded by a vapor layer (which is a reasonable |
| 181 |
> |
assumptions given the initial temperatures of the particles). } |
| 182 |
|
\label{fig:images_cooling_plot} |
| 183 |
|
\end{figure} |
| 184 |
|
|
