| 580 |
|
|
| 581 |
|
\subsection{Langevin Dynamics of Banana Shaped Molecule} |
| 582 |
|
|
| 583 |
< |
In order to compare the |
| 583 |
> |
In order to verify that Langevin dynamics can mimic the dynamics of |
| 584 |
> |
the systems absent of explicit solvents, we carried out two sets of |
| 585 |
> |
simulations and compare their dynamic properties. |
| 586 |
|
|
| 587 |
< |
\begin{figure} |
| 586 |
< |
\centering |
| 587 |
< |
\includegraphics[width=\linewidth]{one_banana.eps} |
| 588 |
< |
\caption[]{.} \label{langevin:banana} |
| 589 |
< |
\end{figure} |
| 587 |
> |
\subsubsection{Simulations Contain One Banana Shaped Molecule} |
| 588 |
|
|
| 589 |
+ |
Fig.~\ref{langevin:oneBanana} shows a snapshot of the simulation |
| 590 |
+ |
made of 256 pentane molecules and one banana shaped molecule at |
| 591 |
+ |
273~K. It has an equivalent implicit solvent model containing only |
| 592 |
+ |
one banana shaped molecule with viscosity of 0.289 center poise. To |
| 593 |
+ |
calculate the hydrodynamic properties of the banana shaped molecule, |
| 594 |
+ |
we create a rough shell model (see Fig.~\ref{langevin:roughShell}), |
| 595 |
+ |
in which the banana shaped molecule is represented as a ``shell'' |
| 596 |
+ |
made of 2266 small identical beads with size of 0.3 $\AA$ on the |
| 597 |
+ |
surface. Applying the procedure described in |
| 598 |
+ |
Sec.~\ref{introEquation:ResistanceTensorArbitraryOrigin}, we |
| 599 |
+ |
identified the center of resistance at $(0, 0.7482, -0.1988)$, as |
| 600 |
+ |
well as the resistance tensor, |
| 601 |
+ |
\[ |
| 602 |
+ |
\left( {\begin{array}{*{20}c} |
| 603 |
+ |
0.9261 & 1.310e-14 & -7.292e-15&5.067e-14&0.08585&0.2057\\ |
| 604 |
+ |
3.968e-14& 0.9270&-0.007063& 0.08585&6.764e-14&4.846e-14\\ |
| 605 |
+ |
-6.561e-16&-0.007063&0.7494&0.2057&4.846e-14&1.5036e-14\\ |
| 606 |
+ |
5.067e-14&0.0858&0.2057& 58.64& 8.563e-13&-8.5736\\ |
| 607 |
+ |
0.08585&6.764e-14&4.846e-14&1.555e-12&48.30&3.219&\\ |
| 608 |
+ |
0.2057&4.846e-14&1.5036e-14&-3.904e-13&3.219&10.7373\\ |
| 609 |
+ |
\end{array}} \right). |
| 610 |
+ |
\] |
| 611 |
+ |
|
| 612 |
|
\begin{figure} |
| 613 |
|
\centering |
| 614 |
|
\includegraphics[width=\linewidth]{roughShell.eps} |
| 618 |
|
|
| 619 |
|
\begin{figure} |
| 620 |
|
\centering |
| 621 |
+ |
\includegraphics[width=\linewidth]{oneBanana.eps} |
| 622 |
+ |
\caption[Snapshot from Simulation of One Banana Shaped Molecules and |
| 623 |
+ |
256 Pentane Molecules]{Snapshot from simulation of one Banana shaped |
| 624 |
+ |
molecules and 256 pentane molecules.} \label{langevin:oneBanana} |
| 625 |
+ |
\end{figure} |
| 626 |
+ |
|
| 627 |
+ |
\subsubsection{Simulations Contain Two Banana Shaped Molecules} |
| 628 |
+ |
|
| 629 |
+ |
\begin{figure} |
| 630 |
+ |
\centering |
| 631 |
|
\includegraphics[width=\linewidth]{twoBanana.eps} |
| 632 |
|
\caption[Snapshot from Simulation of Two Banana Shaped Molecules and |
| 633 |
|
256 Pentane Molecules]{Snapshot from simulation of two Banana shaped |
