| 61 |
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the entire momentum vector $\vec{p}$ or single components of this |
| 62 |
|
vector ($p_x$) between molecules in each of the two slabs. If the two |
| 63 |
|
slabs are separated along the z coordinate, the imposed flux is either |
| 64 |
< |
directional ($J_z(p_x)$) or isotropic ($J_z$), and the response of a |
| 64 |
> |
directional ($j_z(p_x)$) or isotropic ($J_z$), and the response of a |
| 65 |
|
simulated system to the imposed momentum flux will typically be a |
| 66 |
|
velocity or thermal gradient. The transport coefficients (shear |
| 67 |
|
viscosity and thermal conductivity) are easily obtained by assuming |
| 68 |
|
linear response of the system, |
| 69 |
|
\begin{eqnarray} |
| 70 |
< |
J_z(p_x) & = & -\eta \frac{\partial v_x}{\partial z}\\ |
| 70 |
> |
j_z(p_x) & = & -\eta \frac{\partial v_x}{\partial z}\\ |
| 71 |
|
J & = & \lambda \frac{\partial T}{\partial z} |
| 72 |
|
\end{eqnarray} |
| 73 |
|
RNEMD has been widely used to provide computational estimates of thermal |
| 273 |
|
an approach similar to the above would be sufficient for this as well. |
| 274 |
|
|
| 275 |
|
\section{Computational Details} |
| 276 |
+ |
Our simulation consists of a series of systems. |
| 277 |
+ |
|
| 278 |
+ |
A Lennard-Jones fluid system was built and tested first. In order to |
| 279 |
+ |
compare our method with swapping RNEMD, a series of simulations were |
| 280 |
+ |
performed to calculate the shear viscosity and thermal conductivity of |
| 281 |
+ |
argon. 2592 atoms were in a orthorhombic cell, which was ${10.06 \sigma |
| 282 |
+ |
\times 10.06 \sigma \times 30.18 \sigma}$ by size. The reduced density |
| 283 |
+ |
${\rho^* = \rho\sigma^3}$ was thus 0.849, which enabled direct |
| 284 |
+ |
comparison between our results and others. |
| 285 |
+ |
|
| 286 |
+ |
For shear viscosity calculation, the reduced temperature was ${T^* = |
| 287 |
+ |
k_B T / \epsilon = 0.72}$. Simulations were run in microcanonical |
| 288 |
+ |
ensemble (NVE). For the swapping part, Muller-Plathe's algorithm was |
| 289 |
+ |
adopted.\cite{ISI:000080382700030} The simulation box was under |
| 290 |
+ |
periodic boundary condition, and devided into 20 slabs. In each swap, |
| 291 |
+ |
the top slab ${(n = 0)}$ exchange the most negative $x$ momentum with the |
| 292 |
+ |
most positive $x$ momentum in the center slab ${(n = N/2)}$. Referring |
| 293 |
+ |
to Tenney {\it et al.}\cite{tenneyANDmaginn}, a series of swapping |
| 294 |
+ |
frequency were chosen. Corresponding to each result from swapping |
| 295 |
+ |
RNEMD, scaling RNEMD simulations were run with the target momentum |
| 296 |
+ |
flux parameter set to produce a similar momentum flux and shear |
| 297 |
+ |
rate. Furthermore, various scaling frequencies and corresponding flux |
| 298 |
+ |
can be tested for one swapping rate. |
| 299 |
|
|
| 300 |
+ |
After each simulation, the shear viscosities were calculated in |
| 301 |
+ |
reduced unit. |
| 302 |
+ |
|
| 303 |
|
\section{Acknowledgments} |
| 304 |
|
Support for this project was provided by the National Science |
| 305 |
|
Foundation under grant CHE-0848243. Computational time was provided by |
