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 |
+ |
\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]{one_banana.eps} |
624 |
|
|
625 |
|
\begin{figure} |
626 |
|
\centering |
627 |
+ |
\includegraphics[width=\linewidth]{oneBanana.eps} |
628 |
+ |
\caption[Snapshot from Simulation of One Banana Shaped Molecules and |
629 |
+ |
256 Pentane Molecules]{Snapshot from simulation of one Banana shaped |
630 |
+ |
molecules and 256 pentane molecules.} \label{langevin:oneBanana} |
631 |
+ |
\end{figure} |
632 |
+ |
|
633 |
+ |
\subsubsection{Simulations Contain Two Banana Shaped Molecules} |
634 |
+ |
|
635 |
+ |
\begin{figure} |
636 |
+ |
\centering |
637 |
|
\includegraphics[width=\linewidth]{twoBanana.eps} |
638 |
|
\caption[Snapshot from Simulation of Two Banana Shaped Molecules and |
639 |
|
256 Pentane Molecules]{Snapshot from simulation of two Banana shaped |