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\section{Introduction} |
| 84 |
|
|
| 85 |
|
Non-equilibrium Molecular Dynamics (NEMD) methods impose a temperature or velocity {\it gradient} on a |
| 86 |
< |
system,\cite{ASHURST:1975tg,Evans:1982zk,ERPENBECK:1984sp,MAGINN:1993hc,Berthier:2002ij,Evans:2002ai,Schelling:2 |
| 87 |
< |
002dp,PhysRevA.34.1449,JiangHao_jp802942v} and use linear response theory to connect the resulting thermal or |
| 88 |
< |
momentum flux to transport coefficients of bulk materials. However, for heterogeneous systems, such as phase |
| 86 |
> |
system,\cite{ASHURST:1975tg,Evans:1982zk,ERPENBECK:1984sp,MAGINN:1993hc,Berthier:2002ij,Evans:2002ai,Schelling:2002dp,PhysRevA.34.1449,JiangHao_jp802942v} and use linear response theory to connect the resulting thermal or |
| 87 |
> |
momentum flux to transport coefficients of bulk materials. However, for heterogeneous systems, such as phase |
| 88 |
|
boundaries or interfaces, it is often unclear what shape of gradient should be imposed at the boundary between |
| 89 |
|
materials. |
| 90 |
|
|
| 99 |
|
properties, and they have become widely used to compute thermal and mechanical transport in both homogeneous |
| 100 |
|
liquids and solids~\cite{MullerPlathe:1997xw,ISI:000080382700030,Maginn:2010} as well as heterogeneous |
| 101 |
|
interfaces.\cite{garde:nl2005,garde:PhysRevLett2009,kuang:AuThl} |
| 102 |
+ |
|
| 103 |
+ |
The strengths of specific algorithms for imposing the flux between two |
| 104 |
+ |
different slabs of the simulation cell has been the subject of some |
| 105 |
+ |
renewed interest. The original RNEMD approach used kinetic energy or |
| 106 |
+ |
momentum exchange between particles in the two slabs, either through |
| 107 |
+ |
direct swapping of momentum vectors or via virtual elastic collisions |
| 108 |
+ |
between atoms in the two regions. There have been recent |
| 109 |
+ |
methodological advances which involve scaling all particle velocities |
| 110 |
+ |
in both slabs. Constraint equations are simultaneously imposed to |
| 111 |
+ |
require the simulation to conserve both total energy and total linear |
| 112 |
+ |
momentum. The most recent and simplest of the velocity scaling |
| 113 |
+ |
approaches allows for simultaneous shearing (to provide viscosity |
| 114 |
+ |
estimates) as well as scaling (to provide information about thermal |
| 115 |
+ |
conductivity). |
| 116 |
+ |
|
| 117 |
+ |
To date, however, the RNEMD methods have only been usable in periodic |
| 118 |
+ |
simulation cells where the exchange regions are physically separated |
| 119 |
+ |
along one of the axes of the simulation cell. This limits the |
| 120 |
+ |
applicability to infinite planar interfaces. |
| 121 |
|
|
| 122 |
+ |
In order to model steady-state non-equilibrium distributions for |
| 123 |
+ |
curved surfaces (e.g. hot nanoparticles in contact with colder |
| 124 |
+ |
solvent), or for regions that are not planar slabs, the method |
| 125 |
+ |
requires some generalization for non-parallel exchange regions. In |
| 126 |
+ |
the following sections, we present the Velocity Shearing and Scaling |
| 127 |
+ |
(VSS) RNEMD algorithm which has been explicitly designed for |
| 128 |
+ |
non-periodic simulations, and use the method to compute some thermal |
| 129 |
+ |
transport and solid-liquid friction at the surfaces of spherical and |
| 130 |
+ |
ellipsoidal nanoparticles, and discuss how the method can be extended |
| 131 |
+ |
to provide other kinds of non-equilibrium fluxes. |
| 132 |
|
|
| 133 |
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 134 |
|
% **METHODOLOGY** |
| 135 |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
| 136 |
|
\section{Velocity Shearing and Scaling (VSS) for non-periodic systems} |
| 137 |
|
|
| 138 |
< |
The periodic VSS-RNEMD approach uses a series of simultaneous velocity shearing and scaling exchanges between the two |
| 139 |
< |
slabs.\cite{Kuang2012} This method imposes energy and momentum conservation constraints while simultaneously |
| 140 |
< |
creating a desired flux between the two slabs. These constraints ensure that all configurations are sampled |
| 141 |
< |
from the same microcanonical (NVE) ensemble. |
| 138 |
> |
The periodic VSS-RNEMD approach uses a series of simultaneous velocity |
| 139 |
> |
shearing and scaling exchanges between the two slabs.\cite{Kuang2012} |
| 140 |
> |
This method imposes energy and momentum conservation constraints while |
| 141 |
> |
simultaneously creating a desired flux between the two slabs. These |
| 142 |
> |
constraints ensure that all configurations are sampled from the same |
| 143 |
> |
microcanonical (NVE) ensemble. |
| 144 |
|
|
| 145 |
|
\begin{figure} |
| 146 |
|
\includegraphics[width=\linewidth]{figures/npVSS} |
