| 43 |
|
\begin{doublespace} |
| 44 |
|
|
| 45 |
|
\begin{abstract} |
| 46 |
< |
REPLACE ABSTRACT HERE |
| 47 |
< |
With the Non-Isotropic Velocity Scaling (NIVS) approach to Reverse |
| 48 |
< |
Non-Equilibrium Molecular Dynamics (RNEMD) it is possible to impose |
| 49 |
< |
an unphysical thermal flux between different regions of |
| 50 |
< |
inhomogeneous systems such as solid / liquid interfaces. We have |
| 51 |
< |
applied NIVS to compute the interfacial thermal conductance at a |
| 52 |
< |
metal / organic solvent interface that has been chemically capped by |
| 53 |
< |
butanethiol molecules. Our calculations suggest that coupling |
| 54 |
< |
between the metal and liquid phases is enhanced by the capping |
| 55 |
< |
agents, leading to a greatly enhanced conductivity at the interface. |
| 56 |
< |
Specifically, the chemical bond between the metal and the capping |
| 57 |
< |
agent introduces a vibrational overlap that is not present without |
| 58 |
< |
the capping agent, and the overlap between the vibrational spectra |
| 59 |
< |
(metal to cap, cap to solvent) provides a mechanism for rapid |
| 60 |
< |
thermal transport across the interface. Our calculations also |
| 61 |
< |
suggest that this is a non-monotonic function of the fractional |
| 62 |
< |
coverage of the surface, as moderate coverages allow diffusive heat |
| 63 |
< |
transport of solvent molecules that have been in close contact with |
| 64 |
< |
the capping agent. |
| 46 |
> |
We present a new method for introducing stable nonequilibrium |
| 47 |
> |
velocity and temperature gradients in molecular dynamics simulations |
| 48 |
> |
of heterogeneous systems. This method conserves the linear momentum |
| 49 |
> |
and total energy of the system and improves previous Reverse |
| 50 |
> |
Non-Equilibrium Molecular Dynamics (RNEMD) methods and maintains |
| 51 |
> |
thermal velocity distributions. It also avoid thermal anisotropy |
| 52 |
> |
occured in NIVS simulations by using isotropic velocity scaling on |
| 53 |
> |
the molecules in specific regions of a system. To test the method, |
| 54 |
> |
we have computed the thermal conductivity and shear viscosity of |
| 55 |
> |
model liquid systems as well as the interfacial frictions of a |
| 56 |
> |
series of metal/liquid interfaces. |
| 57 |
|
|
| 58 |
|
\end{abstract} |
| 59 |
|
|
| 426 |
|
\multicolumn{2}{c}{$\lambda^*$} & |
| 427 |
|
\multicolumn{2}{c}{$\eta^*$} \\ |
| 428 |
|
\hline |
| 429 |
< |
Swap Interval & Equivalent $J_z^*$ or $j_z^*(p_x)$ & |
| 429 |
> |
Swap Interval $t^*$ & Equivalent $J_z^*$ or $j_z^*(p_x)$ & |
| 430 |
|
NIVS & This work & Swapping & This work \\ |
| 431 |
|
\hline |
| 432 |
|
0.116 & 0.16 & 7.30(0.10) & 6.25(0.23) & 3.57(0.06) & 3.53(0.16)\\ |
| 521 |
|
\includegraphics[width=\linewidth]{velDist} |
| 522 |
|
\caption{Velocity distributions that develop under the swapping and |
| 523 |
|
our methods at high flux. These distributions were obtained from |
| 524 |
< |
Lennard-Jones simulations with $j_z(p_x)\sim 0.4$ (equivalent to a |
| 524 |
> |
Lennard-Jones simulations with $j_z^*(p_x)\sim 0.4$ (equivalent to a |
| 525 |
|
swapping interval of 20 time steps). This is a relatively large flux |
| 526 |
|
to demonstrate the nonthermal distributions that develop under the |
| 527 |
|
swapping method. Distributions produced by our method are very close |
| 576 |
|
300 & 0.8 & 0.815(0.027) & 0.770(0.008) & 0.61 \\ |
| 577 |
|
318 & 0.8 & 0.801(0.024) & 0.750(0.032) & 0.64 \\ |
| 578 |
|
& 1.6 & 0.766(0.007) & 0.778(0.019) & \\ |
| 579 |
< |
& 0.8 & 0.786(0.009)$^a$ & & \\ |
| 579 |
> |
& 0.8 & 0.786(0.009)\footnote{Simulation with $L_z$ |
| 580 |
> |
twice as long.} & & \\ |
| 581 |
|
\hline\hline |
| 582 |
|
\end{tabular} |
| 590 |
– |
$^a$Simulation with $L_z$ twice as long. |
| 583 |
|
\label{spceThermal} |
| 584 |
|
\end{center} |
| 585 |
|
\end{minipage} |
| 591 |
|
temperatures under which our shear viscosity calculations were carried |
| 592 |
|
out covers the liquid range under normal pressure. Our simulations |
| 593 |
|
predict a similar trend of $\eta$ vs. $T$ to EMD results we refer to |
| 594 |
< |
(Table \ref{spceShear}). |
| 594 |
> |
(Table \ref{spceShear}). Considering subtlties such as temperature or |
| 595 |
> |
pressure/density errors in these two series of measurements, our |
| 596 |
> |
results show no significant difference from those with EMD |
| 597 |
> |
methods. Since each value reported using our method takes only one |
| 598 |
> |
single trajectory of simulation, instead of average from many |
| 599 |
> |
trajectories when using EMD, our method provides an effective means |
| 600 |
> |
for shear viscosity computations. |
| 601 |
|
|
| 602 |
|
\begin{table*} |
| 603 |
|
\begin{minipage}{\linewidth} |
| 631 |
|
|
| 632 |
|
[MAY COMBINE JZPX AND JZKE TO RUN ONE JOB BUT GET ETA=F(T)] |
| 633 |
|
[PUT RESULTS AND FIGURE HERE IF IT WORKS] |
| 634 |
< |
\subsection{Interfacial frictions} |
| 635 |
< |
[SLIP BOUNDARY VS STICK BOUNDARY] |
| 636 |
< |
|
| 637 |
< |
qualitative agreement w interfacial thermal conductance |
| 638 |
< |
|
| 639 |
< |
[ETA OBTAINED HERE DOES NOT NECESSARILY EQUAL TO BULK VALUES] |
| 640 |
< |
|
| 641 |
< |
|
| 642 |
< |
[ATTEMPT TO CONSTRUCT BASAL PLANE ICE-WATER INTERFACE] |
| 645 |
< |
|
| 646 |
< |
[FUTURE WORK HERE OR IN CONCLUSIONS] |
| 634 |
> |
\subsection{Interfacial frictions and slip lengths} |
| 635 |
> |
An attractive aspect of our method is the ability to apply momentum |
| 636 |
> |
and/or thermal flux in nonhomogeneous systems, where molecules of |
| 637 |
> |
different identities (or phases) are segregated in different |
| 638 |
> |
regions. We have previously studied the interfacial thermal transport |
| 639 |
> |
of a series of metal gold-liquid |
| 640 |
> |
surfaces\cite{kuang:164101,kuang:AuThl}, and attemptions have been |
| 641 |
> |
made to investigate the relationship between this phenomenon and the |
| 642 |
> |
interfacial frictions. |
| 643 |
|
|
| 644 |
+ |
Table \ref{etaKappaDelta} includes these computations and previous |
| 645 |
+ |
calculations of corresponding interfacial thermal conductance. For |
| 646 |
+ |
bare Au(111) surfaces, slip boundary conditions were observed for both |
| 647 |
+ |
organic and aqueous liquid phases, corresponding to previously |
| 648 |
+ |
computed low interfacial thermal conductance. Instead, the butanethiol |
| 649 |
+ |
covered Au(111) surface appeared to be sticky to the organic liquid |
| 650 |
+ |
molecules in our simulations. We have reported conductance enhancement |
| 651 |
+ |
effect for this surface capping agent,\cite{kuang:AuThl} and these |
| 652 |
+ |
observations have a qualitative agreement with the thermal conductance |
| 653 |
+ |
results. This agreement also supports discussions on the relationship |
| 654 |
+ |
between surface wetting and slip effect and thermal conductance of the |
| 655 |
+ |
interface.[CITE BARRAT, GARDE] |
| 656 |
|
|
| 657 |
|
\begin{table*} |
| 658 |
|
\begin{minipage}{\linewidth} |
| 659 |
|
\begin{center} |
| 660 |
|
|
| 661 |
< |
\caption{Computed interfacial thermal conductance ($G$ and |
| 662 |
< |
$G^\prime$) values for interfaces using various models for |
| 663 |
< |
solvent and capping agent (or without capping agent) at |
| 656 |
< |
$\langle T\rangle\sim$200K. Here ``D'' stands for deuterated |
| 657 |
< |
solvent or capping agent molecules. Error estimates are |
| 658 |
< |
indicated in parentheses.} |
| 661 |
> |
\caption{Computed interfacial friction coefficient values for |
| 662 |
> |
interfaces with various components for liquid and solid |
| 663 |
> |
phase. Error estimates are indicated in parentheses.} |
| 664 |
|
|
| 665 |
< |
\begin{tabular}{llccc} |
| 665 |
> |
\begin{tabular}{llcccccc} |
| 666 |
|
\hline\hline |
| 667 |
< |
Butanethiol model & Solvent & $G$ & $G^\prime$ \\ |
| 668 |
< |
(or bare surface) & model & \multicolumn{2}{c}{(MW/m$^2$/K)} \\ |
| 667 |
> |
Solid & Liquid & $T$ & $j_z(p_x)$ & $\eta_{liquid}$ & $\kappa$ |
| 668 |
> |
& $\delta$ & $G$\footnote{References \cite{kuang:AuThl} and |
| 669 |
> |
\cite{kuang:164101}.} \\ |
| 670 |
> |
surface & model & K & MPa & mPa$\cdot$s & Pa$\cdot$s/m & nm & |
| 671 |
> |
MW/m$^2$/K \\ |
| 672 |
|
\hline |
| 673 |
< |
UA & UA hexane & 131(9) & 87(10) \\ |
| 674 |
< |
& UA hexane(D) & 153(5) & 136(13) \\ |
| 675 |
< |
& AA hexane & 131(6) & 122(10) \\ |
| 676 |
< |
& UA toluene & 187(16) & 151(11) \\ |
| 677 |
< |
& AA toluene & 200(36) & 149(53) \\ |
| 673 |
> |
Au(111) & hexane & 200 & 1.08 & 0.20() & 5.3$\times$10$^4$() & |
| 674 |
> |
3.7 & 46.5 \\ |
| 675 |
> |
& & & 2.15 & 0.14() & 5.3$\times$10$^4$() & |
| 676 |
> |
2.7 & \\ |
| 677 |
> |
Au-SC$_4$H$_9$ & hexane & 200 & 2.16 & 0.29() & $\infty$ & 0 & |
| 678 |
> |
131 \\ |
| 679 |
> |
& & & 5.39 & 0.32() & $\infty$ & 0 & |
| 680 |
> |
\\ |
| 681 |
|
\hline |
| 682 |
< |
bare & UA hexane & 46.5(3.2) & 49.4(4.5) \\ |
| 683 |
< |
& UA hexane(D) & 43.9(4.6) & 43.0(2.0) \\ |
| 684 |
< |
& AA hexane & 31.0(1.4) & 29.4(1.3) \\ |
| 685 |
< |
& UA toluene & 70.1(1.3) & 65.8(0.5) \\ |
| 682 |
> |
Au(111) & toluene & 200 & 1.08 & 0.72() & 1.?$\times$10$^5$() & |
| 683 |
> |
4.6 & 70.1 \\ |
| 684 |
> |
& & & 2.16 & 0.54() & 1.?$\times$10$^5$() & |
| 685 |
> |
4.9 & \\ |
| 686 |
> |
Au-SC$_4$H$_9$ & toluene & 200 & 5.39 & 0.98() & $\infty$ & 0 |
| 687 |
> |
& 187 \\ |
| 688 |
> |
& & & 10.8 & 0.99() & $\infty$ & 0 |
| 689 |
> |
& \\ |
| 690 |
> |
\hline |
| 691 |
> |
Au(111) & water & 300 & 1.08 & 0.40() & 1.9$\times$10$^4$() & |
| 692 |
> |
20.7 & 1.65 \\ |
| 693 |
> |
& & & 2.16 & 0.79() & 1.9$\times$10$^4$() & |
| 694 |
> |
41.9 & \\ |
| 695 |
> |
\hline |
| 696 |
> |
ice(basal) & water & 225 & 19.4 & 15.8() & $\infty$ & 0 & \\ |
| 697 |
|
\hline\hline |
| 698 |
|
\end{tabular} |
| 699 |
< |
\label{modelTest} |
| 699 |
> |
\label{etaKappaDelta} |
| 700 |
|
\end{center} |
| 701 |
|
\end{minipage} |
| 702 |
|
\end{table*} |
| 703 |
|
|
| 704 |
< |
On bare metal / solvent surfaces, different force field models for |
| 705 |
< |
hexane yield similar results for both $G$ and $G^\prime$, and these |
| 706 |
< |
two definitions agree with each other very well. This is primarily an |
| 707 |
< |
indicator of weak interactions between the metal and the solvent. |
| 704 |
> |
An interesting effect alongside the surface friction change is |
| 705 |
> |
observed on the shear viscosity of liquids in the regions close to the |
| 706 |
> |
solid surface. Note that $\eta$ measured near a ``slip'' surface tends |
| 707 |
> |
to be smaller than that near a ``stick'' surface. This suggests that |
| 708 |
> |
an interface could affect the dynamic properties on its neighbor |
| 709 |
> |
regions. It is known that diffusions of solid particles in liquid |
| 710 |
> |
phase is affected by their surface conditions (stick or slip |
| 711 |
> |
boundary).[CITE SCHMIDT AND SKINNER] Our observations could provide |
| 712 |
> |
support to this phenomenon. |
| 713 |
|
|
| 714 |
< |
For the fully-covered surfaces, the choice of force field for the |
| 715 |
< |
capping agent and solvent has a large impact on the calculated values |
| 716 |
< |
of $G$ and $G^\prime$. The AA thiol to AA solvent conductivities are |
| 717 |
< |
much larger than their UA to UA counterparts, and these values exceed |
| 718 |
< |
the experimental estimates by a large measure. The AA force field |
| 719 |
< |
allows significant energy to go into C-H (or C-D) stretching modes, |
| 720 |
< |
and since these modes are high frequency, this non-quantum behavior is |
| 721 |
< |
likely responsible for the overestimate of the conductivity. Compared |
| 722 |
< |
to the AA model, the UA model yields more reasonable conductivity |
| 723 |
< |
values with much higher computational efficiency. |
| 714 |
> |
In addition to these previously studied interfaces, we attempt to |
| 715 |
> |
construct ice-water interfaces and the basal plane of ice lattice was |
| 716 |
> |
first studied. In contrast to the Au(111)/water interface, where the |
| 717 |
> |
friction coefficient is relatively small and large slip effect |
| 718 |
> |
presents, the ice/liquid water interface demonstrates strong |
| 719 |
> |
interactions and appears to be sticky. The supercooled liquid phase is |
| 720 |
> |
an order of magnitude viscous than measurements in previous |
| 721 |
> |
section. It would be of interst to investigate the effect of different |
| 722 |
> |
ice lattice planes (such as prism surface) on interfacial friction and |
| 723 |
> |
corresponding liquid viscosity. |
| 724 |
|
|
| 698 |
– |
\subsubsection{Effects due to average temperature} |
| 699 |
– |
|
| 700 |
– |
We also studied the effect of average system temperature on the |
| 701 |
– |
interfacial conductance. The simulations are first equilibrated in |
| 702 |
– |
the NPT ensemble at 1 atm. The TraPPE-UA model for hexane tends to |
| 703 |
– |
predict a lower boiling point (and liquid state density) than |
| 704 |
– |
experiments. This lower-density liquid phase leads to reduced contact |
| 705 |
– |
between the hexane and butanethiol, and this accounts for our |
| 706 |
– |
observation of lower conductance at higher temperatures. In raising |
| 707 |
– |
the average temperature from 200K to 250K, the density drop of |
| 708 |
– |
$\sim$20\% in the solvent phase leads to a $\sim$40\% drop in the |
| 709 |
– |
conductance. |
| 710 |
– |
|
| 711 |
– |
Similar behavior is observed in the TraPPE-UA model for toluene, |
| 712 |
– |
although this model has better agreement with the experimental |
| 713 |
– |
densities of toluene. The expansion of the toluene liquid phase is |
| 714 |
– |
not as significant as that of the hexane (8.3\% over 100K), and this |
| 715 |
– |
limits the effect to $\sim$20\% drop in thermal conductivity. |
| 716 |
– |
|
| 717 |
– |
Although we have not mapped out the behavior at a large number of |
| 718 |
– |
temperatures, is clear that there will be a strong temperature |
| 719 |
– |
dependence in the interfacial conductance when the physical properties |
| 720 |
– |
of one side of the interface (notably the density) change rapidly as a |
| 721 |
– |
function of temperature. |
| 722 |
– |
|
| 725 |
|
\section{Conclusions} |
| 726 |
< |
[VSIS WORKS! COMBINES NICE FEATURES OF PREVIOUS RNEMD METHODS AND |
| 727 |
< |
IMPROVEMENTS TO THEIR PROBLEMS! ROBUST AND VERSATILE!] |
| 726 |
> |
Our simulations demonstrate the validity of our method in RNEMD |
| 727 |
> |
computations of thermal conductivity and shear viscosity in atomic and |
| 728 |
> |
molecular liquids. Our method maintains thermal velocity distributions |
| 729 |
> |
and avoids thermal anisotropy in previous NIVS shear stress |
| 730 |
> |
simulations, as well as retains attractive features of previous RNEMD |
| 731 |
> |
methods. There is no {\it a priori} restrictions to the method to be |
| 732 |
> |
applied in various ensembles, so prospective applications to |
| 733 |
> |
extended-system methods are possible. |
| 734 |
|
|
| 735 |
< |
The NIVS algorithm has been applied to simulations of |
| 736 |
< |
butanethiol-capped Au(111) surfaces in the presence of organic |
| 737 |
< |
solvents. This algorithm allows the application of unphysical thermal |
| 738 |
< |
flux to transfer heat between the metal and the liquid phase. With the |
| 739 |
< |
flux applied, we were able to measure the corresponding thermal |
| 732 |
< |
gradients and to obtain interfacial thermal conductivities. Under |
| 733 |
< |
steady states, 2-3 ns trajectory simulations are sufficient for |
| 734 |
< |
computation of this quantity. |
| 735 |
> |
Furthermore, using this method, investigations can be carried out to |
| 736 |
> |
characterize interfacial interactions. Our method is capable of |
| 737 |
> |
effectively imposing both thermal and momentum flux accross an |
| 738 |
> |
interface and thus facilitates studies that relates dynamic property |
| 739 |
> |
measurements to the chemical details of an interface. |
| 740 |
|
|
| 741 |
< |
Our simulations have seen significant conductance enhancement in the |
| 742 |
< |
presence of capping agent, compared with the bare gold / liquid |
| 743 |
< |
interfaces. The vibrational coupling between the metal and the liquid |
| 744 |
< |
phase is enhanced by a chemically-bonded capping agent. Furthermore, |
| 745 |
< |
the coverage percentage of the capping agent plays an important role |
| 746 |
< |
in the interfacial thermal transport process. Moderately low coverages |
| 742 |
< |
allow higher contact between capping agent and solvent, and thus could |
| 743 |
< |
further enhance the heat transfer process, giving a non-monotonic |
| 744 |
< |
behavior of conductance with increasing coverage. |
| 741 |
> |
Another attractive feature of our method is the ability of |
| 742 |
> |
simultaneously imposing thermal and momentum flux in a |
| 743 |
> |
system. potential researches that might be benefit include complex |
| 744 |
> |
systems that involve thermal and momentum gradients. For example, the |
| 745 |
> |
Soret effects under a velocity gradient would be of interest to |
| 746 |
> |
purification and separation researches. |
| 747 |
|
|
| 746 |
– |
Our results, particularly using the UA models, agree well with |
| 747 |
– |
available experimental data. The AA models tend to overestimate the |
| 748 |
– |
interfacial thermal conductance in that the classically treated C-H |
| 749 |
– |
vibrations become too easily populated. Compared to the AA models, the |
| 750 |
– |
UA models have higher computational efficiency with satisfactory |
| 751 |
– |
accuracy, and thus are preferable in modeling interfacial thermal |
| 752 |
– |
transport. |
| 753 |
– |
|
| 748 |
|
\section{Acknowledgments} |
| 749 |
|
Support for this project was provided by the National Science |
| 750 |
|
Foundation under grant CHE-0848243. Computational time was provided by |
